# A small flat search coil of area $5cm^{2}$ with 140 closely wound turns is placed between the poles of a powerful magnet producing magnetic field $0.09\; T$ and then quickly removed out of the field region. Calculate(a) change of magnetic flux through the coil, and(b) emf induced in the coil.

(a) The change of magnetic flux through the coil will be given as :

$\Delta \phi =\phi _{2}-\phi _{1}$

$\Delta \phi =0-\phi _{1}\; \; \; (\because \phi _{2}=0)$

$\Delta \phi =0-NBA\cos \theta$

Where, N = 140 = number of turns

B = 0.09 = magnetic field

A = S = Area

Then,

$\Delta \phi =-140\times 0.09\times5\times 10^{-4}\cos \theta$

$\Delta \phi =-63\times 10^{-4}wb$

(b) Now, calculating the induced emf of the coil is given as ;

$e=\frac{-\Delta \phi }{\Delta t}$

$e=\frac{63\times 10^{-4}}{\Delta t}V$

Assuming coil is removed within a millisecond

$e=\frac{63\times 10^{-4}}{10^{-3}}V=6.3V$

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