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  4. The given figure shows infinitely long bent wires in the x-y plane of paper and each carrying a current i. Here O is the origin. Co-ordinates of points P and Q are (2 m, 0) and (6 m , 0), respectively. Magnetic induction at P is given by (α μ0 i/32 π). Find the value of α.

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Q. The given figure shows infinitely long bent wires in the $x-y$ plane of paper and each carrying a current $i$. Here $O$ is the origin. Co-ordinates of points $P$ and $Q$ are $(2 \,m, 0)$ and $(6\, m , 0)$, respectively. Magnetic induction at $P$ is given by $\frac{\alpha \mu_{0} i}{32 \pi}$. Find the value of $\alpha$.Physics Question Image

Moving Charges and Magnetism

Solution:

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Magnetic field at $P$ is only due to portion $A O$ and $B Q$ and direction of field at $P$ due to both section will be same.
$\therefore B_{P}=\frac{\mu_{0} i}{4 \pi \times 2}+\frac{\mu_{0} i}{4 \pi \times 4}=\frac{3 \mu_{0} i}{16 \pi}$