JEE MAIN - Physics (2021 - 17th March Evening Shift - No. 5)
A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?
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$${{{\mu _0}I} \over {4\pi r}}(2 - \pi )$$
$${{{\mu _0}I} \over {2\pi r}}(2 - \pi )$$
$${{{\mu _0}I} \over {4\pi r}}(2 + \pi )$$
$${{{\mu _0}I} \over {2\pi r}}(2 + \pi )$$
Explanation
$$B = {{{\mu _0}I} \over {4\pi r}} + {{{\mu _0}I} \over {4\pi r}} + {{{\mu _0}I} \over {4r}}$$
$$ = {{{\mu _0}I} \over {2\pi r}} + {{{\mu _0}I} \over {4r}}$$
$$ \Rightarrow $$ $$B = {{{\mu _0}I} \over {4\pi r}}(2 + \pi )$$
$$ = {{{\mu _0}I} \over {2\pi r}} + {{{\mu _0}I} \over {4r}}$$
$$ \Rightarrow $$ $$B = {{{\mu _0}I} \over {4\pi r}}(2 + \pi )$$
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