physics experiment electromagnetic induction

20.3 Electromagnetic Induction

Section learning objectives.

By the end of this section, you will be able to do the following:

• Explain how a changing magnetic field produces a current in a wire
• Calculate induced electromotive force and current

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (G) investigate and describe the relationship between electric and magnetic fields in applications such as generators, motors, and transformers.

In addition, the OSX High School Physics Laboratory Manual addresses content in this section in the lab titled: Magnetism, as well as the following standards:

Section Key Terms

Changing magnetic fields.

In the preceding section, we learned that a current creates a magnetic field. If nature is symmetrical, then perhaps a magnetic field can create a current. In 1831, some 12 years after the discovery that an electric current generates a magnetic field, English scientist Michael Faraday (1791–1862) and American scientist Joseph Henry (1797–1878) independently demonstrated that magnetic fields can produce currents. The basic process of generating currents with magnetic fields is called induction ; this process is also called magnetic induction to distinguish it from charging by induction, which uses the electrostatic Coulomb force.

When Faraday discovered what is now called Faraday’s law of induction, Queen Victoria asked him what possible use was electricity. “Madam,” he replied, “What good is a baby?” Today, currents induced by magnetic fields are essential to our technological society. The electric generator—found in everything from automobiles to bicycles to nuclear power plants—uses magnetism to generate electric current. Other devices that use magnetism to induce currents include pickup coils in electric guitars, transformers of every size, certain microphones, airport security gates, and damping mechanisms on sensitive chemical balances.

One experiment Faraday did to demonstrate magnetic induction was to move a bar magnet through a wire coil and measure the resulting electric current through the wire. A schematic of this experiment is shown in Figure 20.33 . He found that current is induced only when the magnet moves with respect to the coil. When the magnet is motionless with respect to the coil, no current is induced in the coil, as in Figure 20.33 . In addition, moving the magnet in the opposite direction (compare Figure 20.33 with Figure 20.33 ) or reversing the poles of the magnet (compare Figure 20.33 with Figure 20.33 ) results in a current in the opposite direction.

Virtual Physics

Faraday’s law.

Try this simulation to see how moving a magnet creates a current in a circuit. A light bulb lights up to show when current is flowing, and a voltmeter shows the voltage drop across the light bulb. Try moving the magnet through a four-turn coil and through a two-turn coil. For the same magnet speed, which coil produces a higher voltage?

• The sign of voltage will change because the direction of current flow will change by moving south pole of the magnet to the left.
• The sign of voltage will remain same because the direction of current flow will not change by moving south pole of the magnet to the left.
• The sign of voltage will change because the magnitude of current flow will change by moving south pole of the magnet to the left.
• The sign of voltage will remain same because the magnitude of current flow will not change by moving south pole of the magnet to the left.

Induced Electromotive Force

If a current is induced in the coil, Faraday reasoned that there must be what he called an electromotive force pushing the charges through the coil. This interpretation turned out to be incorrect; instead, the external source doing the work of moving the magnet adds energy to the charges in the coil. The energy added per unit charge has units of volts, so the electromotive force is actually a potential. Unfortunately, the name electromotive force stuck and with it the potential for confusing it with a real force. For this reason, we avoid the term electromotive force and just use the abbreviation emf , which has the mathematical symbol ε . ε . The emf may be defined as the rate at which energy is drawn from a source per unit current flowing through a circuit. Thus, emf is the energy per unit charge added by a source, which contrasts with voltage, which is the energy per unit charge released as the charges flow through a circuit.

To understand why an emf is generated in a coil due to a moving magnet, consider Figure 20.34 , which shows a bar magnet moving downward with respect to a wire loop. Initially, seven magnetic field lines are going through the loop (see left-hand image). Because the magnet is moving away from the coil, only five magnetic field lines are going through the loop after a short time Δ t Δ t (see right-hand image). Thus, when a change occurs in the number of magnetic field lines going through the area defined by the wire loop, an emf is induced in the wire loop. Experiments such as this show that the induced emf is proportional to the rate of change of the magnetic field. Mathematically, we express this as

where Δ B Δ B is the change in the magnitude in the magnetic field during time Δ t Δ t and A is the area of the loop.

Note that magnetic field lines that lie in the plane of the wire loop do not actually pass through the loop, as shown by the left-most loop in Figure 20.35 . In this figure, the arrow coming out of the loop is a vector whose magnitude is the area of the loop and whose direction is perpendicular to the plane of the loop. In Figure 20.35 , as the loop is rotated from θ = 90° θ = 90° to θ = 0° , θ = 0° , the contribution of the magnetic field lines to the emf increases. Thus, what is important in generating an emf in the wire loop is the component of the magnetic field that is perpendicular to the plane of the loop, which is B cos θ . B cos θ .

This is analogous to a sail in the wind. Think of the conducting loop as the sail and the magnetic field as the wind. To maximize the force of the wind on the sail, the sail is oriented so that its surface vector points in the same direction as the winds, as in the right-most loop in Figure 20.35 . When the sail is aligned so that its surface vector is perpendicular to the wind, as in the left-most loop in Figure 20.35 , then the wind exerts no force on the sail.

Thus, taking into account the angle of the magnetic field with respect to the area, the proportionality E ∝ Δ B / Δ t E ∝ Δ B / Δ t becomes

Another way to reduce the number of magnetic field lines that go through the conducting loop in Figure 20.35 is not to move the magnet but to make the loop smaller. Experiments show that changing the area of a conducting loop in a stable magnetic field induces an emf in the loop. Thus, the emf produced in a conducting loop is proportional to the rate of change of the product of the perpendicular magnetic field and the loop area

where B cos θ B cos θ is the perpendicular magnetic field and A is the area of the loop. The product B A cos θ B A cos θ is very important. It is proportional to the number of magnetic field lines that pass perpendicularly through a surface of area A . Going back to our sail analogy, it would be proportional to the force of the wind on the sail. It is called the magnetic flux and is represented by Φ Φ .

The unit of magnetic flux is the weber (Wb), which is magnetic field per unit area, or T/m 2 . The weber is also a volt second (Vs).

The induced emf is in fact proportional to the rate of change of the magnetic flux through a conducting loop.

Finally, for a coil made from N loops, the emf is N times stronger than for a single loop. Thus, the emf induced by a changing magnetic field in a coil of N loops is

The last question to answer before we can change the proportionality into an equation is “In what direction does the current flow?” The Russian scientist Heinrich Lenz (1804–1865) explained that the current flows in the direction that creates a magnetic field that tries to keep the flux constant in the loop. For example, consider again Figure 20.34 . The motion of the bar magnet causes the number of upward-pointing magnetic field lines that go through the loop to decrease. Therefore, an emf is generated in the loop that drives a current in the direction that creates more upward-pointing magnetic field lines. By using the right-hand rule, we see that this current must flow in the direction shown in the figure. To express the fact that the induced emf acts to counter the change in the magnetic flux through a wire loop, a minus sign is introduced into the proportionality ε ∝ Δ Φ / Δ t . ε ∝ Δ Φ / Δ t . , which gives Faraday’s law of induction.

Lenz’s law is very important. To better understand it, consider Figure 20.36 , which shows a magnet moving with respect to a wire coil and the direction of the resulting current in the coil. In the top row, the north pole of the magnet approaches the coil, so the magnetic field lines from the magnet point toward the coil. Thus, the magnetic field B → mag = B mag ( x ^ ) B → mag = B mag ( x ^ ) pointing to the right increases in the coil. According to Lenz’s law, the emf produced in the coil will drive a current in the direction that creates a magnetic field B → coil = B coil ( − x ^ ) B → coil = B coil ( − x ^ ) inside the coil pointing to the left. This will counter the increase in magnetic flux pointing to the right. To see which way the current must flow, point your right thumb in the desired direction of the magnetic field B → coil, B → coil, and the current will flow in the direction indicated by curling your right fingers. This is shown by the image of the right hand in the top row of Figure 20.36 . Thus, the current must flow in the direction shown in Figure 4(a) .

In Figure 4(b) , the direction in which the magnet moves is reversed. In the coil, the right-pointing magnetic field B → mag B → mag due to the moving magnet decreases. Lenz’s law says that, to counter this decrease, the emf will drive a current that creates an additional right-pointing magnetic field B → coil B → coil in the coil. Again, point your right thumb in the desired direction of the magnetic field, and the current will flow in the direction indicate by curling your right fingers ( Figure 4(b) ).

Finally, in Figure 4(c) , the magnet is reversed so that the south pole is nearest the coil. Now the magnetic field B → mag B → mag points toward the magnet instead of toward the coil. As the magnet approaches the coil, it causes the left-pointing magnetic field in the coil to increase. Lenz’s law tells us that the emf induced in the coil will drive a current in the direction that creates a magnetic field pointing to the right. This will counter the increasing magnetic flux pointing to the left due to the magnet. Using the right-hand rule again, as indicated in the figure, shows that the current must flow in the direction shown in Figure 4(c) .

Faraday’s Electromagnetic Lab

This simulation proposes several activities. For now, click on the tab Pickup Coil, which presents a bar magnet that you can move through a coil. As you do so, you can see the electrons move in the coil and a light bulb will light up or a voltmeter will indicate the voltage across a resistor. Note that the voltmeter allows you to see the sign of the voltage as you move the magnet about. You can also leave the bar magnet at rest and move the coil, although it is more difficult to observe the results.

• Yes, the current in the simulation flows as shown because the direction of current is opposite to the direction of flow of electrons.
• No, current in the simulation flows in the opposite direction because the direction of current is same to the direction of flow of electrons.

Watch Physics

Induced current in a wire.

This video explains how a current can be induced in a straight wire by moving it through a magnetic field. The lecturer uses the cross product , which a type of vector multiplication. Don’t worry if you are not familiar with this, it basically combines the right-hand rule for determining the force on the charges in the wire with the equation F = q v B sin θ . F = q v B sin θ .

Grasp Check

What emf is produced across a straight wire 0.50 m long moving at a velocity of (1.5 m/s) x ^ x ^ through a uniform magnetic field (0.30 T) ẑ ? The wire lies in the ŷ -direction. Also, which end of the wire is at the higher potential—let the lower end of the wire be at y = 0 and the upper end at y = 0.5 m)?

• 0.15 V and the lower end of the wire will be at higher potential
• 0.15 V and the upper end of the wire will be at higher potential
• 0.075 V and the lower end of the wire will be at higher potential
• 0.075 V and the upper end of the wire will be at higher potential

Worked Example

Emf induced in conducing coil by moving magnet.

Imagine a magnetic field goes through a coil in the direction indicated in Figure 20.37 . The coil diameter is 2.0 cm. If the magnetic field goes from 0.020 to 0.010 T in 34 s, what is the direction and magnitude of the induced current? Assume the coil has a resistance of 0.1 Ω. Ω.

Use the equation ε = − N Δ Φ / Δ t ε = − N Δ Φ / Δ t to find the induced emf in the coil, where Δ t = 34 s Δ t = 34 s . Counting the number of loops in the solenoid, we find it has 16 loops, so N = 16 . N = 16 . Use the equation Φ = B A cos θ Φ = B A cos θ to calculate the magnetic flux

where d is the diameter of the solenoid and we have used cos 0° = 1 . cos 0° = 1 . Because the area of the solenoid does not vary, the change in the magnetic of the flux through the solenoid is

Once we find the emf, we can use Ohm’s law, ε = I R , ε = I R , to find the current.

Finally, Lenz’s law tells us that the current should produce a magnetic field that acts to oppose the decrease in the applied magnetic field. Thus, the current should produce a magnetic field to the right.

Combining equations ε = − N Δ Φ / Δ t ε = − N Δ Φ / Δ t and Φ = B A cos θ Φ = B A cos θ gives

Solving Ohm’s law for the current and using this result gives

Lenz’s law tells us that the current must produce a magnetic field to the right. Thus, we point our right thumb to the right and curl our right fingers around the solenoid. The current must flow in the direction in which our fingers are pointing, so it enters at the left end of the solenoid and exits at the right end.

Let’s see if the minus sign makes sense in Faraday’s law of induction. Define the direction of the magnetic field to be the positive direction. This means the change in the magnetic field is negative, as we found above. The minus sign in Faraday’s law of induction negates the negative change in the magnetic field, leaving us with a positive current. Therefore, the current must flow in the direction of the magnetic field, which is what we found.

Now try defining the positive direction to be the direction opposite that of the magnetic field, that is positive is to the left in Figure 20.37 . In this case, you will find a negative current. But since the positive direction is to the left, a negative current must flow to the right, which again agrees with what we found by using Lenz’s law.

Magnetic Induction due to Changing Circuit Size

The circuit shown in Figure 20.38 consists of a U-shaped wire with a resistor and with the ends connected by a sliding conducting rod. The magnetic field filling the area enclosed by the circuit is constant at 0.01 T. If the rod is pulled to the right at speed v = 0.50 m/s, v = 0.50 m/s, what current is induced in the circuit and in what direction does the current flow?

We again use Faraday’s law of induction, E = − N Δ Φ Δ t , E = − N Δ Φ Δ t , although this time the magnetic field is constant and the area enclosed by the circuit changes. The circuit contains a single loop, so N = 1 . N = 1 . The rate of change of the area is Δ A Δ t = v ℓ . Δ A Δ t = v ℓ . Thus the rate of change of the magnetic flux is

where we have used the fact that the angle θ θ between the area vector and the magnetic field is 0°. Once we know the emf, we can find the current by using Ohm’s law. To find the direction of the current, we apply Lenz’s law.

Faraday’s law of induction gives

Solving Ohm’s law for the current and using the previous result for emf gives

As the rod slides to the right, the magnetic flux passing through the circuit increases. Lenz’s law tells us that the current induced will create a magnetic field that will counter this increase. Thus, the magnetic field created by the induced current must be into the page. Curling your right-hand fingers around the loop in the clockwise direction makes your right thumb point into the page, which is the desired direction of the magnetic field. Thus, the current must flow in the clockwise direction around the circuit.

Is energy conserved in this circuit? An external agent must pull on the rod with sufficient force to just balance the force on a current-carrying wire in a magnetic field—recall that F = I ℓ B sin θ . F = I ℓ B sin θ . The rate at which this force does work on the rod should be balanced by the rate at which the circuit dissipates power. Using F = I ℓ B sin θ , F = I ℓ B sin θ , the force required to pull the wire at a constant speed v is

where we used the fact that the angle θ θ between the current and the magnetic field is 90° . 90° . Inserting our expression above for the current into this equation gives

The power contributed by the agent pulling the rod is F pull v , or F pull v , or

The power dissipated by the circuit is

We thus see that P pull + P dissipated = 0 , P pull + P dissipated = 0 , which means that power is conserved in the system consisting of the circuit and the agent that pulls the rod. Thus, energy is conserved in this system.

Practice Problems

The magnetic flux through a single wire loop changes from 3.5 Wb to 1.5 Wb in 2.0 s. What emf is induced in the loop?

What is the emf for a 10-turn coil through which the flux changes at 10 Wb/s?

Check Your Understanding

• An electric current is induced if a bar magnet is placed near the wire loop.
• An electric current is induced if a wire loop is wound around the bar magnet.
• An electric current is induced if a bar magnet is moved through the wire loop.
• An electric current is induced if a bar magnet is placed in contact with the wire loop.
• Induced current can be created by changing the size of the wire loop only.
• Induced current can be created by changing the orientation of the wire loop only.
• Induced current can be created by changing the strength of the magnetic field only.
• Induced current can be created by changing the strength of the magnetic field, changing the size of the wire loop, or changing the orientation of the wire loop.

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Electromagnetic Induction

When a permanent magnet is moved inside of a copper wire coil, electrical current flows inside of the wire. This important physics phenomenon is called electromagnetic induction.

In 1831, the great experimentalist Michael Faraday set out to prove electricity could be generated from magnetism. He created numerous experiments, including the simple but illustrious setup of the copper wire and permanent magnet . Faraday wrapped the copper wire around a paper cylinder and attached the ends of the coil to a galvanometer, which is a device that detects and measures electrical current.

Instructions

• Click and drag the bar magnet back and forth inside the coil.
• Observe the galvanometer and see that there is only current detected when the magnet is in motion.
• Increase the speed of the magnet’s movement (by dragging the magnet faster) to see how this increases the current.
• Add turns to the wire and notice how the reading on the galvanometer increases.
• Flip the magnet. Watch how the direction of the field impacts the direction of the current (depicted with black arrows.)

When the permanent magnet moves inside of the coil, the mechanical energy of the movement is converted into electricity. While this experiment was uncomplicated, it was also revolutionary. Faraday’s work was translated into an equation by James Clerk Maxwell, who went on the expand on Faraday’s findings and create other equations that are the backbone of the study of electromagnetism. Electromagnetic induction is still crucial to the modern world, and is used in devices like generators, transformers, and electric motors. It can also be used to wirelessly charge devices like an electric toothbrush or phone.

To give credit where credit is due, Joseph Henry was not far behind in his independent discovery of electromagnetic induction in 1832. Dig deeper into the history of important scientists in our Pioneers section.

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• Electromagnetism
• Experiment Faraday Henry

Experiments of Faraday and Henry

In this section, we will learn about the experiments carried out by Faraday and Henry that are used to understand the phenomenon of electromagnetic induction and its properties.

Experiment 1:

In this experiment, Faraday connected a coil to a galvanometer, as shown in the figure above. A bar magnet was pushed towards the coil, such that the north pole is pointing towards the coil. As the bar magnet is shifted, the pointer in the galvanometer gets deflected, thus indicating the presence of current in the coil under consideration. It is observed that when the bar magnet is stationary, the pointer shows no deflection and the motion lasts only till the magnet is in motion. Here, the direction of the deflection of the pointer depends upon the direction of motion of the bar magnet. Also, when the south pole of the bar magnet is moved towards or away from the coil, the deflections in the galvanometer are opposite to that observed with the north-pole for similar movements. Apart from this, the deflection of the pointer is larger or smaller depending upon the speed with which it is pulled towards or away from the coil. The same effect is observed when instead of the bar magnet , the coil is moved and the magnet is held stationary. This shows that only the relative motion between the magnet and the coil are responsible for the generation of current in the coil.

Experiment 2:

In the second experiment, Faraday replaced the bar magnet by a second current-carrying coil that was connected to a battery. Here, the current in the coil due to the connected battery produced a steady magnetic field, which made the system analogous to the previous one. As we move the second coil towards the primary coil, the pointer in the galvanometer undergoes deflection, which indicates the presence of the electric current in the first coil. Similar to the above case, here too, the direction of the deflection of the pointer depends upon the direction of motion of the secondary coil towards or away from the primary coil. Also, the magnitude of deflection depends upon the speed with which the coil is moved. All these results show that the system in the second case is analogous to the system in the first experiment.

Experiment 3:

From the above two experiments, it was concluded by Faraday that the relative motion between the magnet and the coil resulted in the generation of current in the primary coil. But another experiment conducted by Faraday proved that the relative motion between the coils was not really necessary for the current in the primary to be generated. In this experiment, he placed two stationary coils and connected one of them to the galvanometer and the other to a battery, through a push-button. As the button was pressed, the galvanometer in the other coil showed a deflection, indicating the presence of current in that coil. Also, the deflection in the pointer was temporary and if pressed continuously, the pointer showed no deflection and when the key was released, the deflection occurred in the opposite direction.

Frequently Asked Questions – FAQs

What is electromagnetic induction, what is a galvanometer.

Galvanometer is a instrument for measuring a small electrical current.

What is the formula to find the ?

• Φ – the amount of magnetic field at a surface
• N is the number of turns in the coil
• e – induced voltage (in volts)

Who discovered electromagnetic induction?

Ac generators works on which principle, what does faraday’s first law of electromagnetic induction state, the below videos help to revise the chapter magnetic effects of electric current class 10.

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Electromagnetic induction.

Students use voltage sensor to measure the maximum emf induced in a coil as a permanent magnet is dropped through it. Students vary the number of loops in the coil and determine how the rate of change of magnetic flux through a coil affects the magnitude and direction of the emf induced in it.

Grade Level: Advanced Placement

Subject: Physics

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• Faraday Electromagnetic Induction Experiment

What is the Electromagnetic Induction Experiment?

Michael Faraday was an English physicist and chemist who lived from September 22, 1791, in Newington, Surrey, England, until August 25, 1867, at Hampton Court, Surrey. Many of his experiments have had a profound effect on electromagnetic knowledge.

Faraday began his career as a pharmacist before becoming one of the leading scientists of the nineteenth century. He discovered a biological novel combination, including benzene, and became the first to 'immerse in gas' permanently. He also published a workbook on practical chemical science showing his strengths in the technical aspects of his business. He invented the first electric motor and dynamo, demonstrated the link between electricity and chemical bonding, identified the effect of magnetism on light, and named diamagnetism, the distinctive behaviour of other things in strong magnetic fields. He laid the experimental and some theoretical groundwork for James Clerk Maxwell's construction of classical electromagnetic field theory.

Electromagnetic Induction

Michael Faraday was the first to discover electromagnetic induction in the 1830s. When Faraday removed a permanent magnet from a coil or single telephone loop, he discovered that ElectroMotive Force or emf, or voltage, had been created, so a stream was generated.

The Galvanometer needle, which is actually the most sensitive center ammeter of a zero-moving coil, will move from its center to one side only if the magnet shown below is pushed "towards" the coil. Because there is no real movement of the magnetic field when the magnet stops moving and is kept upright toward the coil, the galvanometer needle returns to zero.

If the magnet shown below is pulled "towards" the coil, point or needle of the Galvanometer, which is simply the most sensitive center of the zero-moving moving ammeter, it will deviate from its center in only one direction.

The galvanometer needle returns to zero as there is no real movement of the magnetic field when the magnet stops rotating and is kept upright relative to the coil.

The galvanometer needle will also deviate in any direction if the magnet is now held in place and only the coil is moved in or out of the magnet. Moving a coil or wire loop in a magnetic field produces a voltage in the coil, its magnitude relative to the speed or speed of movement. To be sure, Faraday's law requires "related movement" or movement between the coil and the magnetic field, whether magnetic, coil, or both.

Michael Faraday's basic law of electromagnetic induction states that there is a link between electrical energy and a flexible magnetic field. In other words, Electromagnetic Induction is a method of generating electricity and still using magnetic fields in a closed circuit.

So, with magnetism alone, how much voltage (emf) can the coil produce? This is governed by the three conditions listed below.

Increasing the number of coils in the coil - By increasing the number of single conductors across the magnetic field, the amount of emf produced will be the sum of all the coils of the coil, so if the coil is 20 curves, the total number of emf produced will be 20 times more than one wire.

Increase the relative movement between the coil and the magnet - If the same telephone coil moves in the same magnetic field, but the speed or speed is increased, the wire would cut through the flow lines at a faster speed, resulting in more. idud emf.

Increasing the magnetic field - When the same telephone coil is moved at the same speed as a large magnetic field, more emf is produced as more power lines must be cut.

A small endless magnet is rotated by the movement of a bicycle wheel inside a coil that does not turn on small generators like a bicycle dynamo. The electromagnetic voltage provided by the fixed DC voltage can also be made to rotate inside a constant coil, as in large generators generating alternating power in both cases.

The permanent magnet surrounds the middle shaft in a simple dynamo-type generator, and a telephone coil is placed near the rotating magnetic field. The magnetic field surrounding the top and bottom of the coil constantly shifts between the north and south poles as the magnet rotates. According to Faraday's law of electromagnetic induction, this rotating motion of the magnetic field causes an alternating emf in the coil.

Faraday's law states that generating voltage in a conductor can be achieved by transmitting it to the magnetic field or by transmitting the magnetic field past the conductor, and that electrical energy will flow if the conductor is part of a closed circuit. Because it is fitted to the conductor by a magnetic field that changes as a result of the magnetic field, this voltage is known as the inserted emf, which has a negative signal in Faraday's calculations that indicates the direction of the available force.

FAQs on Faraday Electromagnetic Induction Experiment

1. Explain Faraday's Law

Michael Faraday was an English scientist of the 19th century, credited with many great discoveries in the field of physics and chemistry, specifically on the relationship between current and magnets, and electrochemistry. Law of Faraday, by the 19th-century physicist Michael Faraday. This relates the rate of magnetic flux shift through the loop to the magnitude of the electromotive force E caused by the loop. There's a relationship which is stated as - 

E =  dΦ​ / dtE

The electromotive force or EMF refers to the potential difference between the unloaded loop (i.e. when the resistance in the circuit is high). In practice, it is always necessary to regard EMF as a voltage, because both the voltage and the EMF are calculated using the same unit, the volt.

2.  A small 10 mm diameter permanent magnet produces a field of 100 mT. The field drops away rapidly with distance and is negligible more than 1 mm from the surface. If this magnet moves at a speed of 1 m/s through a 100-turn coil of length 1 mm and diameter just larger than the magnet, what is the EMF Induced?

We can use Faraday 's induction law to find the induced EMF. This needs us to know the change in the flow through the coil and how quickly the change is going to happen.

We can start by looking at the cases where the magnet is outside and inside the coil separately. Since we are told that the field decays quickly, we can assume that the flux is zero when the magnet is outside the coil. Since the coil is a close fit around the magnet, we can assume that the field is always orthogonal to the coil and that the flux is orthogonal.

Since the magnet is considered to be traveling at 1000 mm / s, we know that it will be inside a 1 mm long coil for just 1/1000 s (1 ms). So by applying Faraday 's law,

E = -N dΦ / dt 

= - (100 turns) (100. 10 -3 T) (5. 10 -3 m ) 2 / 1. 10 -3 s

• CBSE Class 12 NCERT Solutions

NCERT Solutions for Class 12 Physics Chapter 6 Electromagnetic Induction: Download Free PDF

Ncert solutions class 12 physics chapter 6 electromagnetic induction: this article contains detailed solutions for ncert class 12 physics chapter 6 electromagnetic induction. download exercise solutions for free. .

NCERT Solutions for Class 12 Physics Chapter 6: Physics is considered to be one of the toughest subjects. It is not unusual for students to get afraid of it. Consistent practice is key to mastering physics. Students must regularly practice numerical questions for better understanding and clarity. The exercises given in NCERT textbooks are crucial for preparing students for the examination as there is a chance that the Board exam may carry questions from textbooks. 

To help students, we have provided NCERT Class 12 Physics Chapter 6 Electromagnetic Induction solutions in this article. These solutions have been prepared by the subject matter experts. 

Also Read:   CBSE Class 12 Physics Syllabus 2024-25

Students should study from NCERT Books as they help gain an understanding of concepts and strengthen their basics. These books are recommended due to their explanation of even difficult topics in simple and clear language. 

NCERT Class 12 Physics Chapter 6 Electromagnetic Induction Solutions 

Given below are the questions and solutions from NCERT Class 12 Chapter 6 Electromagnetic Induction. 

EXERCISES 

Q. Predict the direction of induced current in the situations described by the following figures. 

Sol. (a) Direction: qrpq

(b) Direction: prqp; yzxy

(c) Direction: yzxy

(d) Direction: zyxz.

(e) Direction: xryx

(f) Direction: No induced current

Q. Use Lenz’s law to determine the direction of induced current in the situations described by figure (a) A wire of irregular shape turning into a circular shape; (b) A circular loop being deformed into a narrow straight wire.

Sol. According to Lenz’s law (given by German physicist Heinrich Friedrich Lenz), the polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it. Lenz’s law opposes the very cause that causes it. 

(a) Since the passing flux is increasing, the direction of induced current as per Lenz’s law will be: adcb

(b) Since the passing flux is decreasing, the direction of induced current as per  Lenz’s law is: adcba. 

Q. A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?

Sol. Given, 

n = 15 turns / cm

a = 2 sq. cm

Φ=B.A. cosθ…………………………(1)

Initial magnetic field, Bi =μ0nIi

Substituting, 

Bi = (4π x 10-7).(1500).(2)

Or  Bi = 3.77x10-³ T

Final magnetic field, Bf = (4π x 10-7).(1500).(4)

= 7.54x10-³T

Initial value of flux = Bi.A.cos0

= (3.77x10-³).(2x10-⁴)

= 7.54x10-⁷Wb

Final value of flux = Bf.A.cos0

= (7.54x10-³). (2x10-⁴)

= 1.51x10-⁶ Wb

Therefore induced emf

E = Difference in flux / Corresponding time interval

Or E = [(1.51x10-⁶ Wb)–(7.54x10-⁷ Wb)] / 0.1

Or E = 7.56x10-⁶ V

Q. A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s-¹ in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?

length = 8 cm

breadth = 2 cm

velocity = 1 cm / s

Area of the loop

A = 0.0016 sq. m

The loop is moving with the given velocity. As long as the loop lies completely in the magnetic field, no emf will be induced as there is no change in the flux. But the moment it starts slipping into outer space, the flux passing through the loop decreases and an emf is induced. Since the circuit is not complete, current will not flow.

Value of initial flux = BAcos0

= 0.3 x 0.0016

= 0.00048 Wb

Value of final flux = 0, 

(a) In this case the time elapsed is

t = distance / speed

So induced emf

E = (0.00048–0) / 2

Or       E = 2.4x10-⁴V

The voltage will last 2 seconds.

(b) Here the time elapsed is

Thus induced emf

E = 0.00048 / 8

Or    E = 6x10-⁵V

The voltage will last 8 seconds.

Q. A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s-¹ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring. 

w = 400 rad / s

Ф =B.A. cos 0

= 0.5 x 3.14 x 1 x 1

Ф =B.A.cos 180

= -1.571 Wb

Or   f = 400 / 2 x 3.14 = 63.66 / s

E = [ 1.571–(- 1.571)] / 0.0314

Or   E = 100 V

Q. A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s-¹, at right angles to the horizontal component of the earth’s magnetic field, 0.30 x 10-⁴ Wb m-² . (a) What is the instantaneous value of the emf induced in the wire? (b) What is the direction of the emf? (c) Which end of the wire is at the higher electrical potential?

v = 5 m / s

H = 0.3x10-⁴ Wb m²

(a) Einst = Blv

= (0.00003).(10).(5)

= 1.5x10-³ V

(b) West to east

(c)eastern end.

Q. Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit. 

dI = 5–0 = 5 A

Eavg = 200 V

E = L.dI/dt

Substitution gives

Q. A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil? 

d(NФ) / dt = d(MI) / dt

Substituting values, 

d(NФ) = 30 webers

Also, check

CBSE Class 12 Syllabus 2024-2025: Download PDF of All Subjects

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