Question

The toroidal solenoid has $3000$ turns and a mean radius of $10$ cm. It has a soft iron core of relative permeability $2000$. What is the magnitude of the magnetic field in the core when a current of $1$ $A$ is passed through the solenoid?

• A. $19$ T
• B. $12$ T
• C. $5.6$ T
• D. $4.5$ T

Answer 1

The correct option is B $12$ T

Given,

$N=3000$

$r=10cm=0.1m$

$n=\frac{N}{2\pi r}$

${\mu }_r=2000$

$I=1A$

For a solenoid magnetic field, $B=\mu nI={\mu }_r{\mu }_{0}nI$

$B=2000\times 4\pi \times {10}^{-7}\times \frac{N}{2\pi r}\times 1$

$=2000\times 4\times {10}^{-7}\times \frac{3000}{2\pi \times 0.1}\times 1=12T$