A 5.0 nC point charge sits at x = 0. At the same time, a 4100 N/C uniform electric field (created by distant source charges) points in the positive xdirection.
At what point along the xaxis, if any, would a proton experience no net force?
At what point along the xaxis, if any, would an electron experience no net force?
Thanks for the help!!!
1 Answer

Electrostatic force: F = kQq/r²
Electric field force: F = qE
Call the 5 nC charge Q
A proton must naturally lie on the negaive side of the xaxis. Since the
field will pull it in the positive direction while the force from Q pushes it
in the negative direction. To find the distance set these forces equal:
Fnet = qE – kqQ/r² = 0
qE = kqQ/r²
E = kQ/r²
r = √(kQ/E) = √[(9×10⁹Nm²/C²•5×10 ̄ ⁹C)/(4100N/C)] = 10.5 cm
=> Point along xaxis = 10.5 cm
The electron, since it has the same magnitude charge as the proton, will
experience the same forces from Q and the field. So it must also lie on the
same point on the negative xaxis. But the forces are reversed and the field
will instead push it to the negative side and Q will pull it towards the positive
xaxis. The net force for the electron would then look like:
Fnet = kqQ/r² – qE = 0