Question 1

Q1: Predict the direction of induced current in the situations described by the following Figs. 6.15(a) to (f).

Accepted Answer

The direction of the induced current is determined by Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic flux that produced it. (a) The South-pole of the magnet is moving towards the coil. This increases the magnetic flux directed into the...

Question 2

Q2: Use Lenz's law to determine the direction of induced current in the situations described by Fig. 6.16: (a) A wire of irregular shape turning into a ci...

Accepted Answer

According to Lenz's law, the induced current opposes the change in magnetic flux. (a) A wire of irregular shape turning into a circular shape: The magnetic field is directed into the plane of the paper. When the irregular wire turns into a circular shape, its area increases. For a given perimeter, a...

Question 3

Q3: A long solenoid with 15 turns per cm has a small loop of area $2.0 	ext{ cm}^2$ placed inside the solenoid normal to its axis. If the current carried...

Accepted Answer

Given: Number of turns per unit length of the solenoid, $n = 15 	ext{ turns/cm} = 1500 	ext{ turns/m}$ Area of the small loop, $A = 2.0 	ext{ cm}^2 = 2.0 	imes 10^{-4} 	ext{ m}^2$ Initial current, $I_1 = 2.0 	ext{ A}$ Final current, $I_2 = 4.0 	ext{ A}$ Time interval, $\Delta t = 0.1 	ext{ s...

Question 4

Q4: 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...

Accepted Answer

Given: Longer side of the loop, $L = 8 	ext{ cm} = 0.08 	ext{ m}$ Shorter side of the loop, $b = 2 	ext{ cm} = 0.02 	ext{ m}$ Magnitude of the magnetic field, $B = 0.3 	ext{ T}$ Velocity of the loop, $v = 1 	ext{ cm/s} = 0.01 	ext{ m/s}$ To Find: The emf developed ($\varepsilon$) and the dura...

Question 5

Q5: A 1.0 m long metallic rod is rotated with an angular frequency of $400 	ext{ rad s}^{-1}$ about an axis normal to the rod passing through its one end...

Accepted Answer

Given: Length of the metallic rod, $L = 1.0 	ext{ m}$ Angular frequency, $\omega = 400 	ext{ rad/s}$ Magnetic field, $B = 0.5 	ext{ T}$ To Find: The emf developed between the centre and the ring, $\varepsilon$. Formula: Consider a small element of length $dr$ of the rod at a distance $r$ from the...

Question 6

Q6: A horizontal straight wire 10 m long extending from east to west is falling with a speed of $5.0 	ext{ m s}^{-1}$, at right angles to the horizontal...

Accepted Answer

Given: Length of the wire, $l = 10 	ext{ m}$ Speed of the wire, $v = 5.0 	ext{ m/s}$ (falling downwards) Horizontal component of Earth's magnetic field, $B_H = 0.30 	imes 10^{-4} 	ext{ Wb m}^{-2}$ (directed from South to North) To Find: (a) Instantaneous induced emf, $\varepsilon$. (b) Direction...

Question 7

Q7: 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.

Accepted Answer

Given: Initial current, $I_1 = 5.0 	ext{ A}$ Final current, $I_2 = 0.0 	ext{ A}$ Time interval, $\Delta t = 0.1 	ext{ s}$ Average induced emf, $\varepsilon = 200 	ext{ V}$ To Find: The self-inductance of the circuit, $L$. Formula: The relationship between self-inductance, induced emf, and the ra...

Question 8

Q8: 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 link...

Accepted Answer

Given: Mutual inductance, $M = 1.5 	ext{ H}$ Initial current in the first coil, $I_1 = 0 	ext{ A}$ Final current in the first coil, $I_2 = 20 	ext{ A}$ Time interval, $\Delta t = 0.5 	ext{ s}$ (This information is not needed to find the change in flux linkage, but would be needed for the induced...

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