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Question

A circular coil of radius $$10\ cm$$ and $$25$$ turns is rotated about its vertical diameter with an angular speed of $$40rad$$ $${s}^{-1}$$ in a uniform horizontal magnetic field of magnitude $$5\times {10}^{-2}T$$. Calculate the emf induced in the coil. Also, find the current in the coil if the resistance of the coil is $$15\Omega$$.


Solution

$$r=10cm=10\times { 10 }^{ -2 }m$$
$$N=25$$ 
$$\omega =40\ rad{ s }^{ -1 }$$
$$B=5\times { 10 }^{ -2 }T$$
$${ \varepsilon  }_{ 0 }=NBA\omega =25\left( 5\times { 10 }^{ -2 } \right) \times \left[ 3.14\times { \left( 10\times { 10 }^{ -2 } \right)  }^{ 2 } \right] \times 40=1.57V\quad $$
$$I=\cfrac { { \varepsilon  }_{ 0 } }{ R } =\cfrac { 1.57 }{ 15 } =0.1047A\left( I=\cfrac { { \varepsilon  }_{ 0 } }{ R }  \right) $$

Physics

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