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Question

A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in YZ plane. Magnetic field at point O is
712204_4781b38eb7994ae788bd1603be9c9a54.jpg

A
B=μ04πIR(μ^i×2^k)
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B
B=μ04πIR(π^i+2^k)
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C
B=μ04πIR(π^i2^k)
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D
B=μ04πIR(π^i+2^k)
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Solution

The correct option is B B=μ04πIR(π^i+2^k)
Magnetic field due to segment 1
B1=μ0I4πR[sin90+sin0](^k)
=μ0I4πR(^k)=B3
Magnetic field due to segment 2
B2=μ0I4R(^i)=μ0I4πR(π^i)
B at centre
Bc=B1+B2+B3=μ0I4πR(π^i+2^k).

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