Question

Problem 8 I estimate that the Gauss gun (a solenoid) is wound with 500 turns over a distance of 15cm with an average radius of 1.5cm. The peak current is about 300A. Calculate the energy stored in the Gauss’ gun at peak current. Use the infinite solenoid approximation. Select One of the Following: (a) 70J (b) 0.01J (c) 200J (d) 6000J (e) 0.3J

Answer 1

Answer:

Energy stored, U = 66.6 J

Explanation:

It is given that,

Number of turns in the solenoid, n = 500

Radius of solenoid, r = 1.5 cm = 0.015 m

Distance, d = 15 cm = 0.15 m

Let U is the energy stored in the solenoid. Its formula is given by :

$U=\dfrac{1}{2}LI^2$

L is the self inductance of the solenoid

$L=\mu_o N^2A d$

N is the no of turns per unit length

$L=\mu_o (n/d)^2A d$

$L=\dfrac{4\pi\cdot10^{-7}\cdot500^{2}\cdot\pi\cdot\left(0.015\right)^{2}}{0.15}$

L = 0.00148 Henry

$U=\dfrac{1}{2}\times 0.00148\times 300^2$

U = 66.6 J

Out of given options, the correct option for the energy stored in the solenoid is 70 J. So, the correct option is (a) "70 J".