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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Q.

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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a

$\frac{μ_{0} I}{4 π r} (2 + π)$

b

$\frac{μ_{0} I}{4 π r} (2 - π)$

c

$\frac{μ_{0} I}{2 π r} (2 + π)$

d

$\frac{μ_{0} I}{2 π r} (2 - π)$

answer is A.

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Detailed Solution

$F o r s e m i - i n f i n i t e w i r e, B_{1} = \frac{μ_{0} i}{4 π r} F o r s e m i - c i r c l e, B_{2} = \frac{μ_{0} i}{2 r} (\frac{π}{2 π}) F o r s e m i - i n f i n i t e w i r e, B_{3} = \frac{μ_{0} i}{4 π r} (B_{1}, B_{2} & B_{3} a r e i n t o t h e p a p e r) B = B_{1} + B_{2} + B_{3} = \frac{μ_{0} i}{4 π r} (2 + π)$

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