Question

A square frame of $20$ turns wound using a uniform insulated wire of diameter $4$mm is placed plane perpendicular to a uniform magnetic field. Find the current induced in the frame if the field changes at a constant rate of $12$mT per second. Given that the total length of the vertical frame is $4$m and resistivity of the material of the wire is $1.2\mu \Omega m$.

Answer 1

Flux passes through this square as shown in fig.

$\varphi =\overrightarrow{B}.ds$

$=\overrightarrow{B}\left(4^2\right)$

$=16\overrightarrow{B}$

emf induced =$\frac{-dQ}{dt}$

$=-16\frac{d\overrightarrow{B}}{dt}$

$=-16\times 12\times {10}^{-3}$

$e=-192\times {10}^{-3}$ v

Resistance r of the coil is,

$R=N\rho \frac{l}{A}$

where, $l$=length of one turn coil

$A$=area of cross section of coil.

$\rho$=resistivity of material

$N$=total number of turn

$R=20\times 1.2\times {10}^{-6}\times \frac{4\times 4}{\frac{\pi d^2}{4}}$

$=20\times 1.2\times {10}^{-6}\times \frac{4\times 4}{\pi \times 16\times {10}^{-6}}=\frac{56}{\pi }\Omega$