A circular loop of radius r is placed inside along solenoid of radius R (where r < R) with n turns per unit length. If the current in the solenoid changes at a rate dI/dt, what is the induced emf in the loop?

A. _0 n r^2 dIdt — The magnetic field inside the solenoid is uniform and given by B = mu0 n I. The flux through the loop is B times the area of the loop, and the induced emf is the negative rate of change of this flux.

JEE Main · PhysicsHard

$A circular loop of radius r is placed inside along solenoid of radius R (r < R) with n turns per unit length. If the current in the solenoid changes at a rate \frac{d I}{d t}, what is the induced emf in the loop?$

A. $μ_{0} nπ r^{2} \frac{d I}{d t}$
B. $0.5 μ_{0} nπ r^{2} \frac{d I}{d t}$
C. $μ_{0} nπ R^{2} \frac{d I}{d t}$
D. $2 μ_{0} nπ r^{2} \frac{d I}{d t}$

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Correct answer: A — $μ_{0} nπ r^{2} \frac{d I}{d t}$

Solution

Φ = B A = (μ_{0} n I) (π r^{2}) . The induced emf is E = - \frac{d Φ}{d t} = - μ_{0} nπ r^{2} \frac{d I}{d t} . The magnitude is μ_{0} nπ r^{2} \frac{d I}{d t} .

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A circular loop of radius r is placed inside along solenoid of radius R (r<R) with n turns per unit length. If the current in the solenoid changes at a rate dtdI​, what is the induced emf in the loop?

Solution

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More Electromagnetic Induction practice questions

$A circular loop of radius r is placed inside along solenoid of radius R (r < R) with n turns per unit length. If the current in the solenoid changes at a rate \frac{d I}{d t}, what is the induced emf in the loop?$