Question

A proton (m = 1.87 10-7kg) is placed a distance y above a long, horizontal wire of linear charge density. The proton is then released from rest. If the magnitude of the initial occaration of the proton is 3.4x107m / s what is the value of y (in m)? Take AB.8x10 cm K = 9x 10+ N.mc-.to -8.85 x 102 cm

Answer 1

Mass of the proton, m = 1.67 x 10^-27 kg

Charge of proton, q = 1.6 x 10^-19 C

Initial acceleration of the proton, a = 3.4 x 10⁷ m/s²

Acceleration of the proton, a = F/m

Force on the proton, F = ma = 1.67 x 10^-27 x 3.4 x 10⁷ = 5.678 x 10^-20 N

If E is the electric field produced by the line of charge at the point then,

F = qE

Electric field, E = F/q = 5.678 x 10^-20 /1.6 x 10^-19 = 0.355 N/C

Electric field at a point distant y from a line of charge, E = 1/4πε₀ 2λ/y where λ is the linear charge density.

0.355 = 9 x 10⁹ x 2 x λ/y

Distance of the point, y = 50.7 x 10⁹ λ m

The numerical value of y can be found if the linear charge density λ is known.