Question

A long solenoid has $200$ turns per cm and carries a current $i$. The magnetic field at its centre is $6.28 \times 10^{-2}$ weber/$m^2$. 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. $1.05 \times 10^{-2}$ weber/$m^2$
• B. $1.05 \times 10^{-5}$ weber/$m^2$
• C. $1.05 \times 10^{-3}$ weber/$m^2$
• D. $1.05 \times 10^{-4}$ weber/$m^2$

Answer 1

Answer: (A)

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

Answer 2

Magnetic field due to a long solenoid is given by $B=\mu\,_{0}ni$ From given data, $6.28\times10^{-2}=\mu_{0}\times 200\times10^{2}\times i ...\left(i\right)$ and $B=\mu_{0} \times 100\times10^{2} \times\left(i/3\right)...\left(ii\right)$ Solving Eqs.(i) and (ii), we get $B\approx1.05\times10^{-2}\,Wb/m^{2}$