Question

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

• A. $1.05\times {10}^{-2}{\text{Wb/m}}^2$
• B. $1.05\times {10}^{-5}{\text{Wb/m}}^2$
• C. $1.05\times {10}^{-3}{\text{Wb/m}}^2$
• D. $2.1\times {10}^{-4}{\text{Wb/m}}^2$

Answer 1

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

The magnetic field at the centre of a long solenoid is given by,$$B={\mu }_{0}nI$$For first case :

$6.28\times {10}^{-2}={\mu }_0\times 200\times I...\left(1\right)$

For second case:

$B={\mu }_0\times 100\times \frac{I}{3}...\left(2\right)$

From equations $\left(1\right)$ and $\left(2\right)$ we have:

$\frac{B}{6.28\times {10}^{-2}}=\frac{{\mu }_0\times 100\times \frac{I}{3}}{{\mu }_0\times 200\times I}$

$\Rightarrow B=6.28\times {10}^{-2}\times \frac{1}{6}$

$\Rightarrow B\approx 1.05\times {10}^{-2}{\text{Wb/m}}^2$

Hence, option (a) is the correct answer.