Question

A toroid wound with 100 turns/m of wire carries a current of 3 A. the core of toroid is made of iron having relative magnetic peremability of ${\mu }_{r}5000$ under given condition . the magnetic field inside the iron is_____. ( take ${\mu }_0=4\pi \times {10}^{-7}Tm{A}^{-1})$

• A. 0.15 T
• B. 0.47 T
• C. $1.5\times {10}^{-2}T$
• D. 1.88 T

Answer 1

The correct option is D 1.88 T

Given: ${\mu }_r=5000$ //relative permeability//

$I=3A$ //current//

$n=100turns/m$ //n is turns per unit metre//

To find: magnetic field inside the iron is, B=?

Solution: As we know ,

inside torroid, magnetic field is, $B={\mu }_0\ast {\mu }_r\ast n\ast I$

and ${\mu }_o=4\ast \pi \ast {10}^{-7}$ $Tm{A}^{-1}$

$B=4\pi \ast {10}^{-7}\ast 5000\ast 100\ast 3$

$B=60\ast 3.14\ast {10}^{-2}$

$B=1.88T$

hence,

The correct opt: D