JEE Mains · Physics · STD 12 -Electromagnetic induction
- JEE Mains 2020
- Medium
- Numerical
Two concentric circular coils, \(C _{1}\) and \(C _{2}\), are placed in the \(XY\) plane. \(C _{1}\) has \(500\) turns, and a radius of \(1\; cm . C _{2}\) has \(200\) turns and radius of \(20\, cm . C _{2}\) carries a time dependent current \(I(t)=\left(5 t^{2}-2 t+3\right) \;A\) where \(t\) is in \(s\). The \(emf\) nduced in \(C _{1}\) (in \(mV\) ), at the instant \(t =1\; s\) is \(\frac{4}{ x }\). The value of \(x\) is
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Answer & Solution
Correct Answer
(A) \(5\)
Step-by-step Solution
Detailed explanation
\(B =\frac{\mu_{0} NI }{2 R }\)
\(\phi=\frac{\mu_{0} NN ^{\prime} I }{2 R } \pi r ^{2}\)
\(\varepsilon=\frac{ d \phi}{ dt }=\frac{2 \pi \times 10^{-7} \times 10^{5} \times \pi \times 10^{-4}}{0.2}\)
\(=8 \times 10^{-4}=0.8 mV\)
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