Let's say, for example, that an infinite plate generates a constant electric field that exerts a force of 6N on a 1C charge. To move the charge from a distance of 5m to 1m from the plate, the work done is given by 6N * 4m = 24Nm.
The way this has always been explained is that we apply a 6N force over the 4m distance. However, this doesn't make intuitive sense to me:
- If we apply a constant 6N force to the charge in the opposite direction of the electric field, won't the charge simply remain stationary? The force generated by the field and our applied force in the opposite direction should net to zero.
- If the electric field exerts a force of 6N on the charge at every single infinitesimal point along the path from 5m to 1m, when we apply an opposite force of 6N over that same distance, shouldn't the charge simply stay still?
- I think what's troubling me is that I don't see how applying a 6N force can "overcome" the electric field's force and actually move the charge in the opposite direction.
I think the intuition is the same for the force of gravity. A 1kg object that is 1m above the ground is experiencing a force downwards of 10N. If I apply a constant upwards force of 10N, the object won't fall. But how is that if I apply a 10N upwards force over 1m, I can actually move the object upwards? Gravity is exerting a downwards 10N force on the object the entire time I am exerting an upwards 10N force over that 1m. If the forces are equivalent, shouldn't the mass stay still?