Q.

A long wire is bent into the shape PQRST as shown in the following figure with QRS being a semicircle with centre O and radius r metre. A current of I ampere flows through it in the direction P→Q → R → S → T . Then the magnetic induction at the point O of the figure in vacuum is

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a

μ0I2πr-I4r

b

μ0I2r

c

μ0I2πr+I4r

d

μ0I4r

answer is C.

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Detailed Solution

magnetic field due to each of half infinite wire is μ0I4πr and int he same downward direction and field due to semi circle is also downward and has a value μ0I4r
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A long wire is bent into the shape PQRST as shown in the following figure with QRS being a semicircle with centre O and radius r metre. A current of I ampere flows through it in the direction P→Q → R → S → T . Then the magnetic induction at the point O of the figure in vacuum is