Question

Suppose a solenold has inductance L If the number of loops per unit length is increased by a factor of 5.96 , the total number of loops increased by a factor of 7.52 and the area of each loop is increased by a factor of 5.41 by what factor will the inductance be multiplied?

Answer 1

The inductance will be multiplied by 8.62.

Step-by-step explanation:

To find the factor by which the inductance will be multiplied, we need to consider the changes in the number of loops, loops per unit length, and the area of each loop. Let's denote the original inductance as L.

Since the total number of loops is increased by a factor of 7.52, and the number of loops per unit length is increased by a factor of 5.96, the increase in the total number of loops is 7.52 / 5.96 = 1.26 times the original number of loops. This means the number of loops has increased by a factor of 1.26.

The area of each loop is increased by a factor of 5.41, which means the original area has been multiplied by 5.41. Since the inductance is directly proportional to the square of the number of loops and the area, the inductance will be multiplied by (1.26^2) * 5.41 = 8.62 times.