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Question

A wire carrying current I has the shape as adjoining figure. Linear parts of the wire are very long and parallel to Xaxis while semicircular R is lying in YZ plane. Magnetic field at point O is

A
B=μ04πIR(π^i2^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 D B=μ04πIR(π^i+2^k)
Given:- The situation is represented in the figure

To find:- Magnetic field at point O

Solution:- Parallel wires 1 and 3 are semi-infinite, so magnetic field at O due to them
B1=B3=μ0I4πR^k
Now, Magnetic field at O due to semi-circular are in YZ-plane ,
B2=μ0I4R^i
Therefore ,Net magnetic field at point O is given by
B=B1+B2+B3
= -μ0I4πR^kμ0I4R^iμ0I4πR^k
= μ0I4πR(π^i+2^k)

Hence the correct option is D

1993679_1362285_ans_7e17b255475e40d692afbcbc5cd8ff6c.jpeg

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