A pair of stationary and infinitely long bent wires is 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 pallel to the `Y`-axis such that `OS=OR=0.02 m`.Find the magnitude and direction of the magnetic induction at the origin `O`.

Options

A. `10^(-2)Wb//m^(2)` vertically downward
B. `100Wb//m^(2)` vertically upward
C. `10^(-4)Wb//m^(2) ` vertically downward
D. `10^(-4)Wb//m^(2)` vertically upward

Answer

D

Explanation

The point O lies along the same line segemnts Lr and Ms. Hence the restaurant magnetic feild at O due to them is zero. But it is closed to point R and S of the infinite conductors. If OR=OS+X, then the magnetic feild at O due to the segement PR and SQ is `B=B_1 +B_2 =(mu_0)/(4pi)(I/x+I/x)=(mu_0)/(4pi)((2I)/x) = 10^(-7) xx (2 xx 10)/(0.02)=10^(-4)Wb//m^(2) ` This is directed vertically upward along the +ve z-axis. (The wires are in the xy plane.)