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

Answer: (A)

Magnetic field due to a long solenoid is given by
$B=\mu_{0} n i$
From given data,
$6.28 \times 10^{-2}=\mu_{0} \times 200 \times 10^{2} \times i$ ...(i)
and $B=\mu_{0} \times 100 \times 10^{2} \times(i / 3)$ ...(ii)
Solving Eqs. (i) and (ii), we get
$B \approx 1.05 \times 10^{-2} Wb / m ^{2}$