Question

A long solenoid has $200\text{turns/cm}$ and carries a current $i$. The magnetic field at its center is $6.28\times {10}^{-2}\text{T}$. Another long solenoid has $100\text{turns/cm}$ and its carries a current $\frac{i}{3}$. The magnitude of the magnetic field at its center is -

• A. $1.05\times {10}^{-3}\text{T}$
• B. $1.05\times {10}^{-4}\text{T}$
• C. $1.05\times {10}^{-5}\text{T}$
• D. $1.05\times {10}^{-2}\text{T}$

Answer 1

The correct option is D $1.05\times {10}^{-2}\text{T}$

The magnetic field due to a solenoid at its center is given by,

$B={\mu }_{o}ni$

Where,
$n=$ Number of turns per unit length
$i=$ Current flowing in the solenoid

For the first solenoid, magnetic field at its center,

$B_1={\mu }_{o}ni=6.28\times {10}^{-2}\text{T}$

For the other solenoid, magnetic field at its center,

$B_2={\mu }_o{n}^{{}^{\prime }}{i}^{\prime }={\mu }_o\left(\frac{n}{2}\right)\left(\frac{i}{3}\right)$

$=\frac{{\mu }_{o}ni}{6}=\frac{6.28\times {10}^{-2}}{6}=1.05\times {10}^{-2}\text{T}$

Hence, option $\left(D\right)$ is the correct answer.