Questions

# Two infinitely long straight parallel wires are 5 m apart, perpendicular to the plane of paper. One of the wires, as it passes perpendicular to the plane of paper, intersects it at A and carries current i in the downward direction. The other wire intersects the plane A of paper at point B and carries current i in the outward direction O in the plane of paper as shown in figure. With x and y axes as shown, magnetic induction at O in the component form can be expressed as

a
B→=μ0i2π-i^+3j^5
b
B→=μ0i5π-i^+7j^24
c
B→=μ0i4π-3i^+7j^18
d
B→=μ0i7π-2i^+3j^5

detailed solution

Correct option is B

From trigonometry AP = 16/5 and PB - 915. Thus,sin AOP - 4/5 and, cos AOP - 3/5 sin BOP = 3/5 and cos BOP - 4/5 Magnetic field due to A is BA=μ0i8π which makes angle θ with  negative x-axis and lies in third quadrant.  Magnetic field at O due to wire B is BB=μ0i6π which makes   angle θ with y-axis and lies in second quadrant.  In component form BA→=μ0i8π-45i-35j BB→=μ0i6π-35i+45j  Thus, BA→+BB→=μ0i5π-i+724j