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 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 $1.05\times {10}^{-2}Wb/m^2$

$B_1={\mu }_{0}ni$ (for long solenoid)
$\frac{B_1}{B_2}=\frac{n_1\cdot i_1}{n_2\cdot i_2}$
$B_2=\frac{B_1\cdot n_2\cdot i_2}{n_1\cdot i_1}$
$=\frac{6.28\times {10}^{-2}\times 100\times \frac{i}{3}}{200\times i}$
$=1.05\times {10}^{-2}Wb/m^2$