A 800 turn coil of effective area 0.05 is kept perpendicular to a magnetic field . When the plane of the coil is rotated by around any of its coplanar axis in 0.1 , the emf induced in the coil will be [2019]

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Solution

Q.
A 800 turn coil of effective area 0.05 $m^{2}$ is kept perpendicular to a magnetic field $5 \times 10^{- 5} T$ . When the plane of the coil is rotated by $90 °$ around any of its coplanar axis in 0.1 $s$ , the emf induced in the coil will be [2019]

1 0.02 V

2 2 V

3 0.2 V

4 $2 \times 10^{- 3} V$

Ans.
(1)

Here $N = 800,$ $A = 0.05$ $m^{2},$ $Δ t = 0.1$ $s$

$B = 5 \times 10^{- 5} T$

Induced emf, $ε = - \frac{Δ ϕ}{Δ t} = - \frac{(ϕ_{f} - ϕ_{i})}{Δ t}$

$ϕ_{i} = N (\vec{B} \cdot \vec{A}) = 800 \times 5 \times 10^{- 5} \times 0.05 \times \cos 0 ° = 2 \times 10^{- 3} {Tm}^{2}$

$ϕ_{f} = 0 \Rightarrow ∴$ $ε = \frac{- (0 - 2 \times 10^{- 3})}{0.1} = 2 \times 10^{- 2} V = 0.02$ $V$

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