Electromagnetic Induction - Online Test
Q1. Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails,the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T, resistance of the closed loop containing the rod = . Assume the field to be uniform. Suppose K is open and the rod is moved with a speed of 12 cm in the direction shown. Polarity and magnitude of the induced emf are
Answer : Option D
Explaination / Solution:
According to lenz's law P is positive end
Q2. An air-cored solenoid with length 30 cm, area of cross-section 25 and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of s. Average back emf induced across the ends of the open switch in the circuit is
Answer : Option A
Explaination / Solution:
ϕ=NBA=μ0N2Ail|e|=dϕdt
Q3. Expression for the mutual inductance between a long straight wire and a square loop of side a as shown in figure is
Answer : Option D
Explaination / Solution:
dA=adrB=μ04π2irϕ=∫BdA=∫xx+aμ04π2iradrϕ=μ0a2πln(1+1x)
Q4. A straight wire carries a current of 50 A and the loop as in figure is moved to the right with a constant velocity, . Take a and assume that the loop has a large resistance. Induced emf in the loop at the instant when x = 0.2 m is
Answer : Option A
Explaination / Solution:
Q5. Two ends of a horizontal conducting rod of length l are joined to a voltmeter. The whole arrangement moves with a horizontal velocity v, the direction of motion being perpendicular to the rod. Vertical component of the earth's magnetic field is B. The voltmeter reads
Answer : Option C
Explaination / Solution:
Induced EMF is zero because flux linked with it remains constant.
Q6. A horizontal ring of radius r spins about it's axis with an angular velocity ω in a uniform magnetic field of magnitude B. Emf induced in the ring is
Answer : Option B
Explaination / Solution:
Induced EMF is zero because flux linked with it remains constant
Q7. A coil consists of 200 turns of wire having a total resistance of 2.0Ω. Each turn is a square of side 18cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50 T in 0.80 s, Magnitude of the induced emf in the coil while the field is changing is
Answer : Option A
Explaination / Solution:
e=dϕdt
ϕ=NBA
e=200×0.50.8×(18×10−2)2=4.05V
Q8.
An ac generator consists of 8 turns of wire, each of area A=0.0900m2 , and the total resistance of the wire is 12.0Ω. The loop rotates in a 0.500-T magnetic field at a constant frequency of 60.0 Hz. Maximum induced emf is
Answer : Option A
Explaination / Solution:
e=NBAω=NBA2πn=8×0.5×0.09×2×3.14×60=136V
Q9. Assume that a motor in which the coils have a total resistance of 10Ω is supplied by a voltage of 120 V. When the motor is running at its maximum speed, the back emf is 70 V. Current in the coils when the motor is turned on and when it has reached maximum speed are
Answer : Option B
Explaination / Solution:
when motor is turned on
when it has reached maximum speed, the back emf is 70 V then current will be
Q10. The magnetic field between the Horizontal poles of an electromagnet is uniform at any time, but its magnitude is increasing at the rate of 0.020 T/s.The area of a horizontal conducting loop in the magnetic field is 120cm2 , and the total circuit resistance, including the meter, is 5Ω. Induced emf and the induced current in the circuit are
Answer : Option D
Explaination / Solution:
e = Rate of change of magnetic field x area
=0.02×120×10−4=0.24mV
i=eR=0.245=0.48mA
