Question

A circular coil of radius $10\text{cm}$ is placed in a uniform magnetic field of $3.0\times {10}^{–5}\text{T}$ with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of the coil and perpendicular to the magnetic field so that it undergoes half of the rotation in $0.2\text{s}$. The maximum value of $EMF$ induced $\left(\text{in}\mu \text{V}\right)$ in the coil will be close to the integer

Answer 1

Here,$B=3.0\times {10}^{-5}\text{T},R=10\text{cm}=0.1\text{m}$

$\omega =\frac{2\pi }{T}=\frac{2\pi }{2\left(0.2\right)}=\frac{\pi }{0.2}$

Flux as function of time $\varphi =\overrightarrow{B}.\overrightarrow{A}=BA\cos \left(\omega t\right)$

$\text{Emf induced,}E=\frac{-d\varphi }{dt}=BA\omega \sin \left(\omega t\right)$

The maximum value of EMF is given by,

$E_{max}=BA\omega =B\left(\pi R^2\right)\omega$

$\Rightarrow E_{max}=3\times {10}^{-5}\times \pi \times (0.1{)}^2\times \frac{\pi }{0.2}$

$\Rightarrow E_{max}=15\times {10}^{-6}\text{V}$

$\Rightarrow E_{max}=15\mu \text{V}$

Hence, $15$ is the correct answer.