Two parallel wires P and Q placed at a separation d =6 cm on x-axis carry electric current `i_(1) = 5A and i_(2) = 2 A` in opposite directions as shown in Fig. Find the point on the line PQ where the resultant mgnetic field is zero.

Options

A. 4 cm left P
B. 4 cm right of Q
C. middle of PQ
D. At no position

Answer

B

Explanation

At the desired point, the magnetic field due to two wires must have equal magnitude but opposite directions. The point should be either to the left of P or to the right of Q. As the wire Q has smaller current, hte point should be closer to Q. Let this point R be at a distance x form Q.
The magnetic field at R due to the current `i_(1)` will have magnitude.
`(B_1)=(mu_(0)i_(1))/(2 pi (d+x)`
and will be directed in the plane of the figure. The field at the same point due to the current `(i_2)` will be
`B_(2)=(mu_(0)i_(2))/(2 pi x)`
directed upward in the plane of the figure. If the resultant field at R is zero, we should have `B_(1)=B_(2)`, so that `(i_1)/(d+x_=(i_2)/(x)`
Hence, `x=(i_(2)d)/(i_(1)-i_(2)) =((2A)(6 cm))/((3A))=4 cm`.