Question

A 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. $0.012T$
• B. $0.12T$
• C. $1.2T$
• D. $12T$

Answer 1

The correct option is D $12T$

$Given:$ $N=3000$

$r=10cm=0.1m$

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

${\mu }_r=2000$

$I=1A$

$Solution:$

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

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

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

$So,the$ $correct$ $option:D$