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Question

In the given figure, what is the magnetic field induction at point O.
741848_1ccdcb4fcfe74e269059215cafb05266.jpg

A
μ0l4πr
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B
μ0l4r+μ0l2πr
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C
μol4r+μ0l4πr
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D
μ0l4rμ0l4πr
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Solution

The correct option is C μol4r+μ0l4πr
Magnetic field due to straight wire above O is zero
i.e., B1=0(since, θ=0o)
The magnetic field due to semi circular part
B2=(μ0nI2r)=μ0(1/2)I2r=μ0I4r
The magnetic field due to lower straight portion
B3=12μ0I2πr(upward)
Net magnetic field B=B1+B2+B3
=0+μ0I4r+μ0I4πr(upwards).

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