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 due to a long solenoid is given by
$B={\mu }_{0}nI$
given, $6.28\times {10}^{-2}={\mu }_0\times 200\times {10}^2\times I...\left(i\right)$
Also
$B={\mu }_0\times 100\times {10}^2\times \left(\frac{1}{3}\right)...\left(ii\right)$
By solving eqs (i) and (ii) we get
$B=1.05\times {10}^{-2}wb/m^2$