JEE Mains · Physics · STD 12 -6. Electromagnetic induction
A conducting circular loop is placed in \(X - Y\) plane in presence of magnetic field \(\overrightarrow{ B }=\left(3 t ^{3} \hat{ j }+3 t ^{2} \hat{ k }\right)\) in SI unit. If the radius of the loop is \(1 m\), the induced emf in the loop, at time, \(t =2\,s\) is \(n \pi V\). The value of \(n\) is.
- A \(12\)
- B \(6\)
- C \(3\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(12\)
Step-by-step Solution
Detailed explanation
\(\phi=\overrightarrow{ B } \cdot \overrightarrow{ A }\) \(=\left(3 t ^{3} \hat{ j }+3 t ^{2} \hat{ k }\right) \cdot\left(\pi(1)^{2} \hat{ k }\right)\) \(\phi=3 t ^{2} \pi\) \(\varepsilon_{ IDD }=\left|\frac{ d \phi}{ dt }\right|=6 t \pi\) at \(t =2, \varepsilon_{ ID }=12\)
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