Answer to Question #206917 in Electricity and Magnetism for Jake

Question

The plane of a square wire circuit with side 4.0 cm long is at an angle of 45° with respect to a uniform magnetic field of 0.25 T. The wires have a resistance per unit length of 0.2. If the field drops to zero in 2.5 s, what magnitude current is induced in the square circuit?

Answer 1

Gives

Length (l)=4.0cm

Angle($\theta)$ =45°

Magnetic field (B)=0.25T

$\frac{R}{l}=0.2$

Time=3.5sec

Magnetic flux

$$\phi=B.Acos\theta=0.25\times16\times10^{-4}\times cos45°=2\sqrt2\times10^{-4}Wb$$

$e=\frac{d\phi}{dt}$

$$e=\frac{BAcos\theta}{dt}=\frac{2\sqrt2\times10^{-4}}{2.5}=1.131\times10^{-4}Wb/sec$$

Current

$$I=\frac{e}{r}=\frac{1.131\times10^{-4}}{0.2}\times4\times10^{-2}=22.62\times10^{-6}A$$

$I=22.62\mu A$