Question

A solenoid of length 50 cm and a radius of cross-section 1 cm has 1000 turns of wire wound over it. If the current carried is 5 A, the magnetic field on its axis, near the centre of the solenoid is approximately (permeability of free space $ {{\mu }_{0}}~=4\pi \times {{10}^{-7}}T-m/A $ )

• A. $ 0.63\times {{10}^{-2}}T $
• B. $ 1.26\times {{10}^{-2}}T $
• C. $ 2.51\times {{10}^{-2}}T $
• D. 6.3 T

Answer 1

The Correct Option is B

The magnetic field is given by $ B={{\mu }_{0}}ni $ where $ {{\mu }_{0}}=4\pi \times {{10}^{-7}}T\,m{{A}^{-1}}, $ $ n=\frac{1000}{50\times {{10}^{-2}}},i=5A $ $ \therefore $ $ B=4\pi ={{10}^{-7}}\times \frac{1000}{50\times {{10}^{-2}}}\times 5 $ $ B=1.26\times {{10}^{-2}}T $