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Question

A wire bent as shown in Figure carries a current I. Find the magnetic field at P :

142968_8d65bdbd855f48aba48ebc74f6adcd64.png

A
μ0I4R
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B
3μ0I2R
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C
7μ0I8R
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D
μ0I8R
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Solution

The correct option is C μ0I8R
Magnetic field due to the two straight segments of length l at point P are zero respectively.
Magnetic field due to the quarter of circle is 14th of that due to a circular coil.
Magnetic field due to a circular coil is B=μ0I2R where I is current in the coil and R is the radius of the coil.
Hence magnetic field at P due to the quarter segment is B=14×μ0I2R=μ0I8R

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