A solenoid 600 mm long has 50 turns on it and its wound on an iron rod 7.5 mm radius. Find the flux through the solenoid when the current in it is 3A. The relative permeability of iron is 600.

Options

A. 1.66 Wb
B. 1.66 nWb
C. 1.66 mWb
D. 1.66 `mu` Wb

Answer

C

Explanation

`r=7.5 mm = 7.5xx10^(-3)` m
`l=600xx10^(-3)m , N=50, mu_r=mu/mu_0`=600
`therefore mu=600 mu_0, I=3A`
`phi=(muN^2AI)/l =(600mu_0N^2(pir^2)I)/l`
`=(600xx4pixx10^(-7)xx2500xxpixx(7.5xx10^(-3))^2xx3)/(600xx10^(-3))`
`=4pi^2xx2500xx(7.5)^2xx3xx10^(-10)`
`=10^4xx(3.14)^2 xx(7.5)^2 xx 3xx10^10`
`=1.66xx10^(-3)` Wb
=1.66 mWb