Question

A long solenoid has 200 turns per cm and carries a current I. The magnetic field at its centre is $6.28\times {10}^{-2}Wb/m^2$. Another long solenoid has 100 turns per cm and it carries a current i/3. The value of the magnetic field at its centre is

• A. $1.05\times {10}^{-2}Wb/m^2$
• B. $1.05\times {10}^{-5}Wb/m^2$
• C. $1.05\times {10}^{-3}Wb/m^2$
• D. $1.05\times {10}^{-4}Wb/m^2$

Answer 1

The correct option is A $1.05\times {10}^{-2}Wb/m^2$

Magnetic field at the centre of long solenoid $B={\mu }_{o}nI$

where $I$ is the current flowing and $n$ is the number of turns per unit length.

For solenoid 1 :

$n=200$ turns per cm, $B=6.28\times {10}^{-2}$ and $I=i$

$\therefore$ $6.28\times {10}^{-2}={\mu }_o\left(200\right)\left(i\right)$ ....(1)

For solenoid 2 :

$n=100$ turns per cm and $I=i/3$

$\therefore$ $B_2={\mu }_o\left(100\right)\left(i/3\right)$ ....(2)

Divide (2) by (1), we get

$\frac{B_2}{6.28\times {10}^{-2}}=\frac{{\mu }_o\left(100\right)\left(i/3\right)}{{\mu }_o\left(200\right)\left(i\right)}$

$⟹B_2=1.05\times {10}^{-2}Wb/m^2$