Question

A packed bundle of 75 long, straight, insulated wires forms a cylinder of radius R = 0.420 cm. If each wire carries 1.50 A, (a) What is the magnitude of the magnetic force per unit length acting on a wire located 0.220 cm from the center of the bundle?

Answer 1

`42.09\mu N`

Step-by-step explanation:

We are given that

Number of wires= N=75

Radius of cylinder=0.420 cm

Current in each wire=1.5 A

We have to find the magnitude of the magnetic force per unit length acting on a wire located at 0.22 cm from the center of the bundle.

r=0.22 cm

Force acting on a wire is given by

Force=F=IBL

`(F)/(l)=IB=(\mu_0I^2Nr)/(2\pi R^2)`

Substitute the values in the given formula we get

`(F)/(l)=(2\cdot 75\cdot (1.5)^2\cdot 0.220)/((0.42)^2)* (\mu_0)/(4\pi)`

`(F)/(l)=10^(-7)* 420.92`

`F/l=42.09 \mu N`

Hence, force per unit length acting on a wire located 0.22 cm from the center of the bundle=
`42.09\mu N`