First slide

Magnetic flux and induced emf

Question

A circular coil of radius 10cm 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 0.2s. The maximum value of EMF induced in $μ V$ in the coil will be close to the integer

Moderate

Solution

$\begin{array}{l} M a g n e t i c F l u x = ϕ = B . π r^{2} \cos ω t \\ I n d u c e d E M F = ε = - \frac{d ϕ}{d t} = B ω π r^{2} \sin ω t \\ P e a k v a l u e o f e m f = ε_{0} = B ω π r^{2} \\ = 3 \times 10^{- 5} \times (\frac{π}{0.2}) \times π \times 10^{- 2} \\ = \frac{3 π^{2}}{2} μ V ≃ 15 μ V \end{array}$

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