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Question

Physics Question on Magnetism and matter

Figure shows a straight wire length ll carrying current ii. The magnitude of magnetic field produced by the current at point PP is.

A

2μ0iπ1\frac{\sqrt{2\mu_{0}i}}{\pi1}

B

μ0i4π1\frac{\sqrt{\mu_{0}i}}{4\pi1}

C

2μ0i8π1\frac{\sqrt{2}\mu_{0}i}{8\pi1}

D

μ0i22π1\frac{\mu_{0}i}{2\sqrt{2}\pi1}

Answer

2μ0i8π1\frac{\sqrt{2}\mu_{0}i}{8\pi1}

Explanation

Solution

The given situation can be redrawn as follows. As we know the general formula for finding the magnetic field due to a finite length wire

B=μ04πir(sinϕ1+sinϕ2)B=\frac{\mu_{0}}{4 \pi} \cdot \frac{i}{r}\left(\sin \phi_{1}+\sin \phi_{2}\right)
Here, ϕ1=0,ϕ=45\phi_{1}=0^{\circ}, \phi=45^{\circ}
B=μ04πir(sin0+sin45)\therefore B=\frac{\mu_{0}}{4 \pi} \cdot \frac{i}{r}\left(\sin 0^{\circ}+\sin 45^{\circ}\right)
=μ04πi2L=\frac{\mu_{0}}{4 \pi} \cdot \frac{i}{\sqrt{2} L}
B=2μ0i8πl\Rightarrow B=\frac{\sqrt{2} \mu_{0} i}{8 \pi l}