Question

A pair of stationary and infinitely long bent wires are placed in the x-y plane as shown in figure. The wires carry currents of 10A each as shown. The segments L and M are along the x-axis. The segments P and Q are parallel to the y-axis such that OS = OR = 0.02m. Find magnitude and direction of the magnetic induction at the origin O.

• A. $100\,Wb\,m^{-2}$ vertically upward
• B. $10^{-4}\,Wb\,m^{-2}$ vertically downward
• C. $10^{-4}\,Wb\,m^{-2}$ vertically upward
• D. $0.01\,Wb\,m^{-2}$ vertically downward

Answer 1

Answer: (C)

Point O is along the segments L and M, so magnetic field due to them is zero. Point O is near the
end of conductors P and Q. $B_R = B_p + B_Q = \frac{\mu_0 I}{4\pi RO} + \frac{\mu_0 I}{4 \pi SO} = \frac{\mu_0}{4 \pi} \left( \frac{2I}{d}\right)$
Using the given data, $B_R = 10^{-7} \times \frac{2 \times 10}{0.02} = 10^{-4} Wbm^{-2}$ , outside the sheet of paper.