Question

if anyone could explain this to me on the simplest way possible it will be greatly appreciated:

what is the voltage between two points on an equipotential line? will this voltage cause a charge to move along the line?

Answer 1

An equipotential line means the potential is the same or equal along that line. Suppose the potential is V at a point x1 on the equipotential line. Then the potential is also V at another point x2 on the equipotential line. So the voltage between two points or the potential difference between these points on the equipotential lines is P = V - V = 0 (zero).

The work done to move a charge or the change in potential energy of the charge to move across a potential difference P is W = q P, where q is the charge

Now, along the equipotential line P = 0. So work done or change in potential energy of the charged particle if you move along this line is W = 0. Or in other words, there is no force acting on the charge

If the charge is initially at rest ( initially it is not moving) on a point on the equipotential line, then it will remain there forever or it will not move because its change in potential energy is zero and hence its change in kinetic energy will also be zero.

If the charge is initially moving at a speed v along the equipotential line, then it will keep moving forever with speed v along the equipotential line because its change in potential energy is zero and hence its change in kinetic energy will also be zero.

These last two statements are the consequences of Newton's first law of motion.