Question

The value of current is $i$ in the infinite wire forming a shape as shown in the figure. What is the magnetic field at point $O$ at distance $d$ from straight wire segment AB?

• A. $\frac{{\mu }_{0}i}{4\pi d}(\cos \alpha +\cos \beta )$
• B. $\frac{{\mu }_{0}i}{4\pi }\times \frac{2i}{d}$
• C. $\frac{{\mu }_{0}i}{4\pi d}(\sin \alpha +\sin \beta )$
• D. $\frac{{\mu }_{0}i}{4\pi }\times \frac{i}{d}$

Answer 1

The correct option is C $\frac{{\mu }_{0}i}{4\pi d}(\sin \alpha +\sin \beta )$

The field of the wires $AC$ and $BD$ will be zero at point O as it lies on the same line as that of the wire.
The part $AB$ is a conductor with finite length and the magnetic field due to it is given by the formula:

$B=\frac{{\mu }_{0}i}{4\pi d}(\sin \alpha +\sin \beta )$