Chapter 21, Problem 39P

To determine

To find the inductance of a coil.

Answer to Problem 39P

Solution:

The inductance of the coil is 0.105 H.

Explanation of Solution

Given:

Length of the solenoid, l = 0.60 m

Diameter of the solenoid, d = 2.9 cm

Number of loops, N = 8700

Formula used:

$L=\frac{{\mu }_{0}A{N}^2}{l}=\frac{{\mu }_0\pi d^2{N}^2}{4l}$

Calculation:

We know that the inductance (L)of the solenoid is given by the relation,

$L=\frac{{\mu }_{0}A{N}^2}{l}=\frac{{\mu }_0\pi d^2{N}^2}{4l}$

Substituting the given values in the above relation, we get,

$L=\frac{4\pi \times {10}^{-7}\times \pi \times {\left(\text{2}\text{.9}\times {10}^{-2}\right)}^2\times {8700}^2}{\text{4 }\times \text{ 0}\text{.6}}=0.105\text{ H}$