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A tangent galvanometer shows a deflection $45^{o}$ when 10 mA current pass through it. If the horizontal component of the earth's fleld is $3.6 x 10^{- 5} T$ and radius of the coil is 10 cm, the number of turns in the coil is

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5700 turns

57 turns

570 turns

5.7 turns

answer is C.

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Detailed Solution

$\begin{array}{rcl} tanθ & = & \frac{μ_{0} ni}{2 B_{H} r} \\ n & = & \frac{2 B_{H} tanθ}{μ_{0} i} \\ = & \frac{2 x 36 x 10^{- 5} x 10 x 10^{- 2}}{4 πx 10^{- 7} x 10 x 10^{- 3}} \tan 45^{0} \\ n & = & 572.9 \approx 570 \end{array}$

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