Question

A long solenoid with radius 2 cm carries a current of 2A. The solenoid is 70 cm long and is composed of 300 turns of wire. Calculate flux linked with a circular surface if it has radius greater than 2 cm and axis of solenoid subtends an angle of $60^\circ$ with the normal to the area (the centre of circular surface being on the axis of solenoid)

• A. $6\times10^{-6}\,Wb$
• B. $5\times10^{-5}\,Wb$
• C. $6.76\times10^{-7}\,Wb$
• D. $7.6\times10^{-7}\,Wb$

Answer 1

Answer: (C)

$6.76\times10^{-7}\,Wb$

Answer 2

For an ideal solenoid $B_{\text{out}}$ = 0 and $B_{\text{in}} = \frac{\mu_0}{4 \pi} . 4 \pi \frac{Ni}{l}$ $=\frac{4 \pi \times 10^{-7} \times 300 \times 2}{0.7} = 1.076 \times 10^{-3} \,T$. And $\phi = BA \,cos \,\theta$ or $\phi = \phi_{\text{in}} + \phi_{\text{out}}$ $= B_{\text{in}} \times (\pi r^2) \times \, cos\, 60\,{\circ} + 0$ $( \because \, B_{\text{out}} = 0)$ $= 1.076 \times 10^{-3}) \times ( \pi \times 4 \times 10^{-4}) \times \frac{1}{2}$ $= 13.52 \times 10^{-7} \times \frac{1}{2} = 6.76 \times 10^{-7}\, Wb$