Chapter 21, Problem 83GP

To determine

Rate of change of magnetic field

Answer to Problem 83GP

Solution:

It can be need to solution $\frac{\Delta B}{\Delta t}=3279.52\text{T/s}$

Explanation of Solution

Given:

Number of turns of the coil $N=35$

Diameter of the coil $d=12.5\text{cm}$

Induced emf $\epsilon =120\text{V}$

Formula Used:

$\left|\epsilon \right|=N\frac{\Delta {\varphi }_B}{\Delta t}$

Calculation:

If $\frac{\Delta B}{\Delta t}$ be the rate at which the field change then

$\begin{array}{l}\left|\epsilon \right|=N\frac{\Delta {\varphi }_B}{\Delta t}=N\frac{A\Delta B}{\Delta t}\\ \frac{\Delta B}{\Delta T}=\frac{\left|\epsilon \right|}{N(\pi d^2/4)}\end{array}$

$\begin{array}{l}\frac{\Delta B}{\Delta t}=\frac{4\times 120}{35\pi ({0.125}^2)}\text{T/s}\\ \frac{\Delta B}{\Delta t}=279.52\text{T/s}\end{array}$