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Question: A closely wound coil of 100 turns and area of cross-section \(1\mspace{6mu} cm^{2}\) has a coefficie...

A closely wound coil of 100 turns and area of cross-section 1 6mucm21\mspace{6mu} cm^{2} has a coefficient of self-induction 1 mH. The magnetic induction in the centre of the core of the coil when a current of 2A flows in it, will be

A

0.022 6muWbm−20.022\mspace{6mu} Wbm^{- 2}

B

0.4 6muWb 6mum−20.4\mspace{6mu} Wb\mspace{6mu} m^{- 2}

C

0.8 6muWb 6mum−20.8\mspace{6mu} Wb\mspace{6mu} m^{- 2}

D

1 6muWb 6mum−21\mspace{6mu} Wb\mspace{6mu} m^{- 2}

Answer

0.022 6muWbm−20.022\mspace{6mu} Wbm^{- 2}

Explanation

Solution

B=μ0Ni2r=4π×10−7×100×2×π2×10−2=0.022 6muwb/m2B = \frac{\mu_{0}Ni}{2r} = \frac{4\pi \times 10^{- 7} \times 100 \times 2 \times \sqrt{\pi}}{2 \times 10^{- 2}} = 0.022\mspace{6mu} wb/m^{2}