Question

An infinitely long line of charge has a linear charge density of 8.00×10 ⁻¹²

C/m A proton is at distance How close does the proton get to the line of charge? 16.5 cm from the line and is moving directly toward the line with speed 2100 m/s Express your answer in meters.

Answer 1

To find out how close the proton gets to the line of charge, we use the electric field of a line of charge and equate the proton's initial kinetic energy to its potential energy at the turnaround point.

Step-by-step explanation:

The question asks about the minimum distance a proton moving towards an infinitely long line of charge will get before it stops and turns around. Given the linear charge density of the line of charge and the initial velocity of the proton, we can determine this distance by applying concepts of electric fields and energy conservation to the proton's motion.

The electric field E created by an infinitely long line of charge is given by the equation E = (2kλ)/r, where k is the Coulomb's constant, λ is the linear charge density, and r is the distance from the line. The force on the proton is F = Ee, where e is the elementary charge on the proton. When the proton comes to a stop, all its initial kinetic energy has been converted into electric potential energy due to the work done against the electric field. By equating the proton's initial kinetic energy with its potential energy at the turnaround point, we can solve for the minimum distance r from the charge line.