Question:
A conducting circular loop is placed in X -Y plane in presence of magnetic field
\(\stackrel{→}{B} = (3t^3\hat{j}+3t^2\hat{k})\) in SI unit. If the radius of the loop is 1 m, the induced emf in the loop at time \(t = 2s\) is \(nπV\). The value of \(n\) is ______.
A conducting circular loop is placed in X -Y plane in presence of magnetic field
\(\stackrel{→}{B} = (3t^3\hat{j}+3t^2\hat{k})\) in SI unit. If the radius of the loop is 1 m, the induced emf in the loop at time \(t = 2s\) is \(nπV\). The value of \(n\) is ______.
\(\stackrel{→}{B} = (3t^3\hat{j}+3t^2\hat{k})\) in SI unit. If the radius of the loop is 1 m, the induced emf in the loop at time \(t = 2s\) is \(nπV\). The value of \(n\) is ______.
Updated On: Mar 19, 2025
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Correct Answer: 12
Solution and Explanation
The correct answer is 12
\(B_⊥=3t^2\)
\(\frac{dB_⊥}{dt} = 6t = 12 at\ t = 2\)
\(\frac{d\phi_1}{dt} = 12×π(1)^2\)
\(= 12π\)
Therefore , value of \(n\) is 12.
\(B_⊥=3t^2\)
\(\frac{dB_⊥}{dt} = 6t = 12 at\ t = 2\)
\(\frac{d\phi_1}{dt} = 12×π(1)^2\)
\(= 12π\)
Therefore , value of \(n\) is 12.
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Concepts Used:
Faradays Laws of Induction
There are two laws, given by Faraday which explain the phenomena of electromagnetic induction:
Faraday's First Law:
Whenever a conductor is placed in a varying magnetic field, an emf is induced. If the conductor circuit is closed, a current is induced, known as the induced current.
Faraday's Second Law:
The Emf induced inside a coil is equal to the rate of change of associated magnetic flux.
This law can be mathematically written as:
∈\(-N {\triangle \phi \over \triangle t}\)
