Question

An infinitely long line of charge has a linear charge density of 3.00×10^?12 C/m . A proton is at distance 12.5 cm from the line and is moving directly toward the line with speed 1100 m/s .

`How close does the proton get to the line of charge?

Answer 1

calculate the kinetic energy of photon,

K = 1/2*mp*v^2

K = 0.5 x 1.67 x 10^-27 x (1100)^2

K = 1.01 x 10^-21 J

Apply the law of conservation of energy

K1 + U1 = K2 + U2

where, K2 = 0 , U = -ve

K1 = U2 - U1

K1 = e(V1 - V2)

The electric potential at a diatance r from the infinitely long line of charge,

V1 - V2 = ( / 2pi*eo)*(r2/r1)

K1 = e* ( / 2pi*eo)*ln(r2/r1)

ln(r2/r1) = K1*2pi*eo / *e

ln(r2/r1) = (1.01 x 10^-21 x 2pi x 8.854 x 10^-12) / (3 x 10^-12 x 1.6 x 10^-19)

ln(r2/r1) = 0.1171

r1 = 12.5 cm / 1.124

r1 = 11.12 cm