Question

A magnetic field of magnitude B(t) = B, et pierces the loop shown in the figure in a direction perpendicular to the plane of the loop. Bo = 3.33 T and 8 = 2.22 s-1. The loop is made of cylindrical copper wire, whose radius is r=0.444 mm. The resistivity of copper is p=1.68 x 1089.m. The radius of the loop is 12.2 cm. What is the magnitude of the emf induced in the loop at time t = 0.844 s? R

Answer 1

Given,

Magnetic field is  $\large B = B_0 e^{\beta t}$

where $\large B_0 = 3.33 \ T$ and  

1 B= 2.22 s

Radius of loop is  

R= 12.2 cm 0.122 m

Area of loop is  $\large A = \pi R^2 = \pi * 0.122^2 = 0.0468 \ m^2$

The magnetic flux linked with the coil is

$\large \phi = BA = AB_0 e^{\beta t}$

The emf induced in the loop is given by,

$\large \\\epsilon = \frac{d\phi}{dt} \\\\\epsilon = \frac{d(AB_0 e^{\beta t})}{dt} \\\\\epsilon = AB_0\frac{d(e^{\beta t})}{dt} \\\\\epsilon = AB_0 * e^{\beta t} * \beta \\\\\epsilon = 0.0468 * 3.33 * e^{(2.22 * 0.844)} * 2.22 \\\\\epsilon = 0.346 * e^{1.87} \\\\\epsilon = 2.245 \ V$