`AB` and `CD` are long staright conductors, distance `d` apart, carrying a current `I`. The magnetic field on `BC` due to the currents in `AB` and `CD`

Options

A. is zero at all points
B. is zero at this midpoint
C. has different magnitudes at different points
D. is maximum at its midpoints

Answer

C

Explanation

Magnetic field at `P`,
Due to `①, B_(1)=(mu_(0)I)/(4pix), ox`
Due to `②, B_(2)=(mu_(0)I)/(4pi(d-x)), ox`
`B_(P)=B_(1)+B_(2)=(mu_(0)I)/(4pi)[1/x+1/(d-x)]`
`=(mu_(0)I)/(4pi).d/(x(d-x)), ox`
`x(d-x)` is maximum if
`x=d-x` i.e, `x=d//2`
At `x=d/2` (mid-point of `BC`), magnetic field is minimum.