PQ and RS are long parallel conductors separated by certain distance. M is the midpoint between them (see the figure). The net magnetic field at M is B. Now the current 2 A is switched off. The field at M now becomes

Options

A. `2B`
B. B
C. `B/2`
D. `3B`

Answer

B

Explanation

Magnetic field at midpoint /m due to current in PQ is
`B_(PQ)=(mu_(0)xx2xx2)/(4pid)=(4mu_(0))/(4pid)` . . .(i)
Magnetic field at M due to current in RS is
`B_(RS)=(mu_(0)xx2xx1)/(4pid)=(2mu_(0))/(4pid)` . . .(ii)
The net magnetic field at midpoint M is
`B=B_(PQ)-B_(RS)(becauseB_(PQ)" and "B_(RS)" are in opposite direction")`
`=(4mu_(0))/(4pid)-(2mu_(0))/(4pid)=(2mu_(0))/(4pid)` . . . (iii)
when the current 2 A is switched off, the net magnetic field at M is due to current 1 A
`B.=(mu_(0)xx2xx1)/(4pid)=B" (Using (iii))"`