1.
Calculate the magnetic flux through a square loop of side 10 cm placed perpendicular to a uniform magnetic field of 0.5 T.
2.
A circular coil of radius 5 cm is placed in a magnetic field of 0.2 T such that the normal to the coil makes an angle of 60° with the field lines. Find the magnetic flux linking the coil.
3.
State Faraday's laws of electromagnetic induction mathematically and conceptually.
4.
The magnetic flux through a coil changes from 10 Wb to 2 Wb in 0.1 s. Calculate the magnitude of the average induced EMF.
5.
A coil of 100 turns has a flux of $5 \times 10^{-3}$ Wb linking it. If the magnetic flux is completely reduced to zero in 0.05 s, find the induced EMF.
6.
Why does a galvanometer show a momentary deflection when a bar magnet is suddenly pushed into a coil connected to it?
7.
The magnetic flux linked with a coil is given by the equation $\Phi = 3t^2 + 4t + 9$ Wb. Find the magnitude of the induced EMF at $t = 2$ s.
8.
Define the SI unit of magnetic flux. Is it a scalar or a vector quantity?
9.
How does the induced EMF in a coil change if the speed of relative motion between the coil and a magnet is doubled?
10.
A rectangular loop of area $0.04 \text{ m}^2$ is kept exactly parallel to a uniform magnetic field of 0.8 T. What is the magnetic flux through the loop?
11.
State Lenz’s law of electromagnetic induction.
12.
"Lenz's law is a direct consequence of the law of conservation of energy." Explain this statement briefly.
13.
A North pole of a magnet is brought rapidly towards a closed conducting loop. What will be the direction of the induced current in the face of the loop pointing towards the magnet?
14.
If a horizontal copper ring is held steady and a bar magnet is dropped vertically through it (North pole pointing down), what is the direction of the induced current in the ring as viewed from above?
15.
In the scenario above (Question 14), will the acceleration of the falling magnet be equal to, greater than, or less than $g$? Give a reason.
16.
Two identical closed loops, one made of copper and one of constantan (higher resistance), are subjected to the exact same changing magnetic flux. In which loop will the induced EMF be greater?
17.
Referring to Question 16, in which of the two loops will the induced current be greater? Justify using Ohm's Law.
18.
A straight wire is dropped horizontally, remaining parallel to the ground, falling across the Earth's horizontal magnetic field. Will an EMF be induced across its ends?
19.
Explain conceptually why it requires mechanical effort (work) to rapidly pull a closed conducting loop out of a strong uniform magnetic field.
20.
A closed loop is placed in a time-varying magnetic field. Does the magnitude of the induced current depend on the cross-sectional area of the wire used to make the loop? Justify.
21.
Derive the expression $E = Blv$ for the motional EMF induced in a straight conductor moving perpendicular to a uniform magnetic field.
22.
A 0.5 m long conducting rod is moved at a constant speed of 4 m/s perfectly perpendicular to a uniform magnetic field of 0.2 T. Calculate the induced motional EMF.
23.
An airplane with a wingspan of 40 m flies horizontally at a speed of 360 km/h. If the vertical component of the Earth's magnetic field is $4 \times 10^{-5}$ T, calculate the EMF induced between the wingtips.
24.
A conducting rod of length $L$ rotates with uniform angular velocity $\omega$ about one end, perpendicular to a uniform magnetic field $B$. Write the formula for the induced EMF across its ends.
25.
A metal spoke of a wheel of length 0.8 m rotates at 120 rev/min in a plane normal to a uniform magnetic field of 0.5 T. Calculate the exact EMF induced between the axle and the rim.
26.
State the specific hand rule used to find the direction of induced current in a straight conductor moving in a magnetic field.
27.
What is the mechanical power required to move a straight conducting rod of length $l$ and resistance $R$ with constant velocity $v$ in a perpendicular magnetic field $B$?
28.
If the velocity of a moving rod in a uniform magnetic field is halved, how does the magnitude of the motional EMF change?
29.
A railway track runs North-South. Will an EMF be induced across the axle of a train running on it due to the Earth's magnetic field? Which component of the Earth's field is responsible?
30.
Is motional EMF fundamentally caused by an induced electric field or a magnetic Lorentz force? Explain briefly.
31.
What are eddy currents? Describe the basic condition required for them to be produced.
32.
State two significant disadvantages of eddy currents in large electrical machines like transformers and motors.
33.
How exactly are eddy currents minimized in the iron core of a transformer? Explain the mechanism.
34.
Briefly explain how eddy currents are purposefully utilized in the magnetic braking systems of high-speed trains.
35.
How does an induction furnace use the principle of eddy currents to melt metals and alloys?
36.
Why are the metallic pendulum plates in dead-beat galvanometers often cut with deep slots?
37.
A solid copper cube and a laminated copper block of the identical dimensions are allowed to oscillate in a strong magnetic field. Which one will come to rest faster and why?
38.
Do eddy currents obey Lenz's Law? Give a brief conceptual reason to support your answer.
39.
Name one medical or real-world application of electromagnetic damping/heating (other than trains or galvanometers).
40.
If the electrical resistance of a bulk metal is significantly increased, how does it physically affect the magnitude of the eddy currents produced within it?
41.
Define self-inductance of a coil. Write its SI unit.
42.
The current in a primary coil drops from 5 A to 0 A in 0.1 s, inducing an average EMF of 200 V in the coil itself. Calculate the self-inductance of the coil.
43.
Write the standard formula for the self-inductance ($L$) of a long ideal air-cored solenoid of length $l$, cross-sectional area $A$, and number of turns $N$.
44.
Calculate the self-inductance of an air-cored solenoid 50 cm long, having a radius of 2 cm and 500 total turns. ($\mu_0 = 4\pi \times 10^{-7} \text{ T}\cdot\text{m/A}$)
45.
Define mutual inductance between two neighboring coils.
46.
Two coaxial solenoids have a mutual inductance of 1.5 H. If the current in the primary solenoid changes at a steady rate of 4 A/s, what is the EMF induced in the secondary?
47.
Calculate the magnetic potential energy stored in an inductor of 50 mH carrying a steady direct current of 2 A.
48.
On what structural and physical factors does the mutual inductance of a pair of coaxial solenoids primarily depend?
49.
How does inserting a soft iron core completely inside an air-cored solenoid affect its self-inductance?
50.
Conceptually, why is the property of self-induction often referred to in physics as the "inertia of electricity"?
51.
State the underlying physical principle of an AC generator.
52.
Write the mathematical formula for the instantaneous EMF ($e$) induced in an AC generator. Briefly define all the terms in the formula.
53.
A circular coil of an AC generator has 100 turns, an area of $0.05 \text{ m}^2$, and rotates at exactly 50 rev/s in a uniform magnetic field of 0.2 T. Calculate the peak induced EMF.
54.
What is the mechanical and electrical function of the slip rings in an AC generator?
55.
At what specific physical position of the rotating coil (relative to the magnetic field) is the induced EMF in an AC generator maximum?
56.
How does the peak EMF of an AC generator change if the angular speed of rotation ($\omega$) is doubled while keeping all other factors constant?
57.
State the mathematical shape of the EMF vs. time graph for a standard AC generator operating at a constant speed.
58.
If an electrical generator is designed to produce direct current (DC) instead of alternating current (AC), what specific mechanical component replaces the slip rings?
59.
An AC generator produces a peak EMF of 314 V at a frequency of 50 Hz. Write the complete trigonometric equation for the instantaneous EMF $e(t)$.
60.
Does the average EMF produced by an AC generator over one complete rotational cycle equal zero? Provide a mathematical reason.
