A long straight wire lies on a horizontal table and carries

A long, straight wire lies on a horizontal table and carries a current of 1.60 µA. In a vacuum, a proton moves above and parallel to the wire (opposite the current) with a constant speed of 2.15 x 10^4 m/s at a distance d from the center of the wire. Determine the value of d. Ignore the magnetic field due to the Earth. (The mass of proton is 1.67 x 10^-27 kg, and the charge of proton is 1.6 x 10^-19 C.)

Solution

on proton:

gravitation force = magnetic force due to wire

(as Fnet on proton is zero. )

magnetic force = q v B

and B = u0 I / (2 pi d )

m g = q v u0 I / (2 pi d )

1.67 x 10^-27 x 9.81 = (1.6 x 10^-19 x 2.15 x 10^4 x 4pi x 10^-7 x 1.60 x 10^-6) / (2 pi d )

d = 0.0701 m Or 7.01 cm .......Ans