Question

A piece of wire of cross-sectional area A and resistivity ρ is bent into a circular loop of radius r and placed in a magnetic field with its plane at right angles to the field. Determine the magnitude of the current in the loop if the field is reduced to zero in time t.

Answer 1

$Given:\\A-cross-sectional\ area,\\\rho-resistivity,\\ r-radius\ of\ the\;loop,\\t-time \\Solution:\\E_i=|\frac{\Delta\Phi}{\Delta t}|=|\frac{(0-B)S}{t}|=\frac{BS}{t};\\I=\frac{E_i}{R}; R=\rho\frac{l}{A}; S=\pi r^2;\Rightarrow I=\frac{B rA}{t \rho}\\without\ taking\ into\\ account\ the\ direction\ of\ the\ current\\Answer:\\ I=\frac{B rA}{t \rho}$