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  4. The coil in a tangent galvanometer is 16 cm in radius. If a current of 20 mA is to produce a deflection of text4 text5 texto, then the number of turns wound on it, is (Take horizontal component of earths magnetic field =0.36× 10-4T and μ 0=4π × 10-7 WbA-1m-1 )

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Q. The coil in a tangent galvanometer is 16 cm in radius. If a current of 20 mA is to produce a deflection of $ \text{4}{{\text{5}}^{\text{o}}}, $ then the number of turns wound on it, is (Take horizontal component of earths magnetic field $ =0.36\times {{10}^{-4}}T $ and $ {{\mu }_{0}}=4\pi \times {{10}^{-7}}\,Wb{{A}^{-1}}{{m}^{-1}} $ )

WBJEEWBJEE 2006

Solution:

Current in coil of tangent galvanometer $ i=\frac{2rH}{{{\mu }_{0}}n}\tan \theta $ $ \Rightarrow $ $ n=\frac{2rH}{{{\mu }_{0}}i}\tan \theta $ $ \therefore $ $ n=\frac{2\times 16\times {{10}^{-2}}\times 0.36\times {{10}^{-4}}}{4\pi \times {{10}^{-7}}\times 20\times {{10}^{-3}}}\tan {{45}^{o}} $ $ =458 $