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If I separate some amount of positive and negative charge a certain distance I will create some voltage. If I then separate the same amount of positive and negative charge a longer distance I will create an even bigger voltage since more work would've been needed to separate them.

Now, the charges with a larger potential difference will experience less of a force of attraction because they're farther apart, and the charges with a lower potential difference will experience a larger force of attraction since they are closer together.

Question 1: If voltage is a measure of the "push" acting on charge, then how can this be so?

Question 2: Voltage is proportional to current. But in this case I would think that the lower voltage scenario would produce higher current because there's a stronger force acting on the charge. What's going on? How does potential difference produce current?

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The electric field is a measure of the "push" acting on an electric charge. The voltage (aka electrical potential) is a measure of the energy required to move an electric charge from one location to another location in an electric field. There is an analogy with gravity: the gravitational field at your location is a measure of the "pull" you feel. The gravitational potential is a measure of the energy required to move your body from the bottom of a ladder to the top of the ladder.

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