Answer to Question #117499 in Electricity and Magnetism for Peace

Question

A uniform magnetic field 0.50T is directed at an angle of 60° to the plane of a 100 turn, rectangular cooper coil of length 0.04m and width 0.05m. The diameter of the copper wires which makes up the coils is 1.00mm and the resistivity of copper is 1.7 * 10^-8 ohmmeter. The magnetic field through the loop decreases to zero in 0.3s. Determine
(I.) The initial flux through the coil.
(ii.) The average induced e.m.f in the coil as the field decreases

Answer 1

As per the question,

magnetic field $(B)=0.50T$

angle $(\theta)=60^\circ$

Number of turn $(n)=100$

Length of the copper coil $(l)=0.04m$

width $(w)=0.05m$

diameter of the coil $(d)=1.0mm=1\times 10^{-3}m$

resistivity $(\rho)=1.7 \times 10^-8 \Omega -meter$

$\dfrac{dB}{dt}=0.5/0.3=1.5T/sec$

so, initial flux through the coil = $nB.A$

$=100\times 0.50\times 0.04\times0.05=100\times 0.0020\times0.5=1T-m^2$

induced emf $=N\dfrac{-dB}{dt}A=100\times 1.5\times0.0020 =0.3V$