An infinitely long straight conductor is bent into the shape as shown in the fig

Question

An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at its centre will be

Options:

A . μ04π2ir(π+1)

B . μ04π.2ir(π−1)

C . Zero

D . Infinite

Answer: Option B
:
B
The given shape is equivalent to the following diagram
The field at o due to straight part of conductor is

B_{1} = \frac{μ_{0}}{4 π} . \frac{2 i}{r} ⊙

The field at o due to circular coil is

B_{2} = \frac{μ_{0}}{4 π} . \frac{2 π i}{r} \otimes

. Both fields will act in the opposite direction, hence the total field at O.
i.e.

B = B_{2} - B_{1} = (\frac{μ_{0}}{4 π}) \times (π - 1) \frac{2 i}{r} = \frac{μ_{0}}{4 π} . \frac{2 i}{r} (π - 1)

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