Two parallel beams of protons and electrons, carrying equal currents are fixed at a separation d. The protons and electrons move in opposite directions. There is a point P on the straight perpendicular line joining the two beams at a distance x from one beam. The magnetic field at this point is B. If B is plotted against x, it can be represented by the curve.

Options

A.
B.
C.
D.

Answer

B

Explanation

The two parallel beams of protons and electrons will be equivalent to two linear parallel line wires carrying currents in the same direction. The resultant magnetic field at P is

`B=(mu_0)/(4pi)(2I)/(x)-(mu_0)/(4pi)(2I)/((d-x))=(mu_0)/(4pi)2I[1/x-(1)/(d-x)]`
If `x=d//2`, `B=0`. If `xltd//2`, B is positive and if `x gt d//2` then B is negative. Thus variation between B and x will be represented by option (b).