JEE Mains · Physics · STD 12 -Electromagnetic induction
- JEE Mains 2020
- Hard
- Numerical
A circular coil of radius \(10\, cm\) is placed in a uniform magnetic field of \(3.0 \times 10^{-5}\, T\) with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in \(0.2\,s.\) The maximum value of \(EMF\) induced (in \(\mu V\) ) in the coil will be close to the integer\(....\mu V\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(15\)
Step-by-step Solution
Detailed explanation
\(r=0.1 m \quad \frac{ T }{2}=0.2 sec\)
\(B =3 \times 10^{-5} m \quad T =0.4 sec\)
At any time
\(flux \phi= BA \cos \omega t\)
\(| emf |=\left|\frac{ d \phi}{ dt }\right|=| BA \omega \sin \omega t |\)
\(( emf )_{\max }= BA \omega= BA \quad \frac{2 \pi}{ T }\)
\(=\frac{3 \times 10^{-5} \times \pi \times(0.1)^{2} \times 2 \pi}{0.4}\)
\(=\frac{6 \pi^{2}}{4} \times 10^{-6}\) \(\left(\begin{array}{c}\pi^{2}=10 \text { take }\end{array}\right)\)
\(=15 \times 10^{-6}\)
\(=15 \mu V\)
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