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 solenoid has $100$ turns per $cm$ and it carries a current $\frac{i}{3}$. The value of the magnetic field at its centre :

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

Answer 1

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

Let,
$B_1=6.28\times {10}^{-2}Wb{m}^{-2}$,
$n_1=200$,
$n_2=100$
and $B_2$ is the magnetic field at the center of other solenoid.

For solenoid, $B\propto ni$
$\Rightarrow B_1\propto n_1{i}_1$ and $B_2\propto n_2{i}_2$
Therefore we can write
$\frac{B_2}{B_1}=\frac{n_2{i}_2}{n_1{i}_1}$
$B_2=B_1\frac{n_2{i}_2}{n_1{i}_1}$
$B_2=6.28\times {10}^{-2}\times \frac{100\left(\frac{i}{3}\right)}{200i}$
$B_2=\frac{6.28\times {10}^{-2}}{6}=1.05\times {10}^{-2}Wb{m}^{-2}$