A metal rod of length 1 meter rotates about one end with an angular velocity of 20 radians per second in a uniform magnetic field of 0.5 Tesla directed perpendicular to the plane of rotation. What is the induced electromotive force between the ends of the rod?

A. 5 V — The induced EMF in a rotating rod is given by the formula epsilon = 0.5 * B * omega * l squared. Substituting the given values, we get 0.5 * 0.5 * 20 * 1 squared = 5 V.

JEE Main · PhysicsMedium

$A metal rod of length $l = 1 \text{ m}$ rotates about one end with an angular velocity $\omega = 20 \text{ rad/s}$ in a uniform magnetic field $B = 0.5 \text{ T}$ directed perpendicular to the plane of rotation. What is the induced electromotive force $\varepsilon$ between the ends of the rod?$

A. $5 \text{ V}$
B. $10 \text{ V}$
C. $2.5 \text{ V}$
D. $20 \text{ V}$

Show correct answer & step-by-step solution

Correct answer: A — $5 \text{ V}$

Solution

The induced EMF is

ε = \int_{0}^{l} B ω r d r = \frac{1}{2} B ω l^{2}

. Substituting the values,

ε = 0.5 \times 0.5 \times 20 \times 1^{2} = 5 V

Attempt this question & track your score

Attempt & Track Free →

More Electromagnetic Induction practice questions

A magnetic flux of 500 Weber passes through a coil of 10 turns in 0.1 seconds. What is the magnitude of the induced elec
Lenz's law is a consequence of the law of conservation of which physical quantity?
A conducting rod of length 1 meter moves with a velocity of 2 meters per second perpendicular to a magnetic field of 0.5
The self-inductance of a coil is 2 Henry. If the current in the coil changes at a rate of 5 Amperes per second, what is
Which of the following units is equivalent to the Weber?
A circular coil of radius 10 cm and 500 turns is placed in a uniform magnetic field of 0.5 T such that the plane of the
A square loop of side 10 cm and resistance 0.5 ohm is moved out of a magnetic field of 1 Tesla at a constant velocity of
Two coils have a mutual inductance of 0.005 Henry. If the current in the primary coil changes from 5 Ampere to 2 Ampere
A solenoid of length 0.5 m has 1000 turns and across-sectional area of 10 square centimeters. What is the self-inductanc
A square loop of side length Land resistance R is placed in a time-varying magnetic field B = B0 sin(omega t) directed p
A conducting rod of length L rotates with angular velocity omega about one end in a uniform magnetic field B perpendicul
A solenoid of length l, radius r, and n turns per unit length carries a current I = I0 cos(omega t). The induced electri

View all Electromagnetic Induction questions →