Electromagnetic Induction Important Questions

Very Short Answer Questions [1 Mark Questions]

Ques. What is the SI unit of magnetic flux?

Ans. The SI unit of magnetic flux is Weber (Wb) or Tesla Square Meter (T m²).

Ques. Write the working principle of dynamo.

Ans. A dynamo works on the principle of electromagnetic induction, which states that when a coil rotates in the presence of a uniform magnetic field, current is induced in it.

Ques. Where does the inductor store energy?

Ans. The inductor stores energy in its magnetic field. The following expression tells about that

E = 1/2 LI₀²

Where L is the inductance of the inductor and I₀ is the maximum value of current.

Ques. What is the self-inductance of a straight conductor?

Ans. In the case of a coil, self-inductance can be observed, since the coil has a certain number of turns. In the case of a straight conductor, the number of turns is zero. Because self-inductance is related to the number of coil turns, therefore the self-inductance of a straight conductor is always zero.

Ques. What is electromagnetic induction?

Ans. Whenever the magnetic flux linked with an electric circuit changes an e.m.f. is induced in the circuit. The phenomenon is called electromagnetic induction.

Ques. Whenever a magnet is moved either towards or away from a conducting coil an e.m.f. is induced, the magnitude of which is independent of

1. the speed with which the magnet is moved
2. the strength of the magnetic field
3. the resistance of the coil
4. the number of turns in the coil 

Ans. The correct answer is c. the resistance of the coil.

Explanation: The magnitude of emf induced whenever a magnet is moved either toward or away from a conducting coil is given by

ε = -N dΦ/dt = -N d(BA)/dt

From the above expression, it is clear that induced emf depends on the number of turns of the coil (N), the strength of the magnetic field (B), the area of the cross-section of the coil (A), and the time interval (dt) which depends on the velocity (v) with which the magnet is moved. It is independent of the resistance of the coil. 

Ques. What is the principle of electromagnetic induction based on?

Ans. Lenz's law is based on the principle of conservation of energy. According to the definition of Lenz's law, the induced current is always resisted by the cause that creates it. As a result, there is additional work done against the opposing force.

Ques. How can you increase the energy stored in an inductor by 4 times?

Ans. Let initially, the energy stored in an inductor is, E_i = 1/2 LI_i²

The final energy stored in the inductor is, E_f = 1/2 LI_f²

When the energy stored in the inductor becomes 4 times the initial value i.e. E_f = 4E_i, then

E_f = 4E_i = 1/2 LI_f²

⇒ 4 x 1/2 LI_i² = 1/2 LI_f²

⇒ I_f = 2I_i

Hence when the current is doubled, the energy stored in the inductor becomes 4 times.

Ques. What is Faraday's first law of electromagnetic induction?

Ans. Faraday’s first law of electromagnetic induction states that when there is a relative motion between coil and magnet an e.m.f. is induced across the coil. This induced e.m.f. lasts as long as the change in magnetic flux continues in the coil.

Ques. What is the second Faraday's law of electromagnetic induction?

Ans. Faraday’s second law of electromagnetic induction states that the magnitude of induced e.m.f. is directly proportional to the rate of change of magnetic flux.

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Short Answer Questions [2 Marks Questions]

Ques. What is the magnetic flux? State its SI unit.

Ans. The magnetic flux through any surface placed in a magnetic field is the total number of magnetic lines passing through that surface. It is denoted by ϕ or ϕ_B

Magnetic flux through the surface is given by

ϕ_B = BA cosθ

The SI unit of magnetic flux is Weber (Wb) or Tesla Square Meter (T m²). 

Ques. State the second law of electromagnetic induction.

Ans: The magnitude of induced e.m.f is directly proportional to rate of change in magnetic flux

e ∝ dϕ/dt

E = -dϕ/dt

The SI unit of magnetic flux is weber/ tesla-metre

Ques. What are the methods of generating induced emf?

Ans:

• Induced emf by changing the magnetic field B
• Induced emf by changing the area of coil
• Induced emf by changing the relative orientation of the coil and the magnetic field

Ques. What are the factors on which self inductance depends?

Ans: L = (μ₀ N² A) / l

• It depends on number of turns N
• It depends on area of cross section A
• Permeability of core material μ0

Ques. What is the lenz’ s law ?

Ans: According to Lenz's law , the polarity of the induced e.m.f. is such that it opposes the change in the magnetic flux responsible for its production.

Ques. When the current changes from +2A to – 2A in 0.05s, an e.m.f of 8V is induced in the coil. The coefficient of self induction of coil is?

Ans: Given – L = 8v

E = | L dI/dT |

E = (8 V × 0.05) /4

E = 0.1 H

Ques. Two coils of self inductance 2mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coil is?

Ans: Given – L₁ = 2 mH

L₂ = 8 mH

M = √(L₁ × L₂)

M = √(2 × 8)

M = 4 mH

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Long Answer Questions [3 Marks Questions]

Ques. A 100 mH coil carries a current of 1 A. Energy stored in the form of magnetic field is 

Ans: Given – L = 100 mH

I = 1 A

E = ½ LI²

E = ½ 100 × 10^-3 × 1

E = 50 × 10^-3 J

Ques. In an a.c generator, a coil with N turns all of the same area A and total resistance R, rotates with frequency ω in a magnetic field B. What is the maximum value of e.m.f. generated in coil ?

Ans: |E| = |-dϕ/dt|

E = dϕ/dt

E = d (NBA cos θ)/ dt

E = NBA sinθ dθ/dt

E = NABω -------------------------- ω = dθ/dt , sinθ= 1

Ques. A long solenoid has 500 turns. When a current of 2A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is 4×10^-3 Wb. The self inductance of the solenoid is

Ans: Given – Φ = 500 turns × 4×10^-3 Wb

I = 2 A

Φ = LI

L = ϕ/I

L = 500 × 4 × 10^-3/ 2

L = 1000 ×10^-3 H

L = 1 H

Ques. The current in a self inductance L = 40mH is to be increased uniformly from the 1 A to 11 A in 4 milliseconds. The e.m.f. induced in the inductor during the process is ?

Ans: Given – L = 40mH

dt = 4 milliseconds 

dI = 11 – 1 = 10

|E| = |-L dI/dt|

E = (40 × 10^-3 × 10 ) / 4 × 10^-3 ----------------------- dI = 11-1=10

E = 100 V

Ques. In EMI, why is the induced emf not dependent on the résistance of the coil?

Ans:  E = -dϕ/dt [ϕ = NBA cosθ]

dϕ – change of flux

dt – change of time 

N – number of turns

B – Magnetic energy

Does not depend on resistance of coil

According to above equation it seems that it is independent of resistance of coil 

When you write E = IR and finding current then there will be role of resistance

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Very Long Answer Questions [5 Marks Questions]

Ques. A conducting circular loop is placed in a uniform magnetic field B = 0.025 T with its plane perpendicular to the field. The radius of the loop is made to shrink at a constant rate 1 mm s^-1. The induced e.m.f. when the radius is 2 cm is ?

Ans: Given - B = 0.025 T

R = 2 cm

dR/dt = 1 mm s^-1

The direction of B and A is same 

|E| = |-dϕ/dt|

E = dϕ/dt

E = d (BA cos 0)/ dt

E = B cos0 dA/dt

E = B d(πR²)/ dt 

E = B π2R dR/dt

E = 0.025 × π × 2 × 2 × 10^-4 × 1 ×10^-3

E = π × 10^-6 V

E = π μV

Ques.A magnetic field of 2 × 10^-2 T acts at right angles to a coil of area 100 cm² with 50 turns. The average e.m.f. induced in the coil is 0.1v, when it is removed from the field in the time t. the value of t is ?

Ans: Given – N = 50

B = 2 × 10^-2 T

A = 100 cm²

E = 0.1 v

|E| = |-dϕ/dt|

|E| = |ϕ₂ – ϕ₁/dt|

dt = |0 – NBA cos0 / 0.1| -------------------------- 0˚ because it acts as a right angle of a coil

dt = |0 – 50 × 2 ×10^-2 × 100 × 10^-4 cos0/ 0.1|

dt = 0.1 s

Ques. What is mutual induction?

Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation I = I₀ Sin ωt, where I₀ = 10 A and ω = 100 π rad^-1 . Then what is the maximum value of e. m. f. in the second coil ?

Ans:

Mutual inductance – When two coils are brought in proximity with each other then the magnetic field in one of the coils tends to link with the other coil. This leads to generation of voltage in the second coil. This property of the coil that affects or changes the current and voltage in the secondary coil is called mutual inductance. 

Given – M = 0.005 H

I₀ = 10 A and ω = 100 π rad^-1

E = |M dI/ dt|

E = |M d I₀ Sin ωt / dt|

E = 0.005 × I₀ cos ωt × ω

E_max = 0.005 × I₀ × ω

E_max = 0.005 × 10 × 100π

E_max = 5π

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