An infinitely long line of charge has a linear charge density of 7.50×10^−12 c/m . a proton is at distance 14.5 cm from the line and is moving directly toward the line with speed 3000 m/s . how close does the proton get to the line of charge? express your answer in meters.

10.22 cm

Explanation:

linear charge density, λ = 7.5 x 10^-12 C/m

distance from line, r = 14.5 cm = 0.145 m

initial speed, u = 3000 m/s

final speed, v = 0 m/s

charge on proton, q = 1.6 x 10^-19 C

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

Let the closest distance of proton is r'.

The potential due t a line charge at a distance r' is given  by

where, K = 9 x 10^9 Nm^2/C^2

W = q V

By use of work energy theorem

Work = change in kinetic energy

By substituting the values, we get

r' = 14.5 x 0.7047 = 10.22 cm