![]() ![]() A chemical reaction near the negative terminal of a battery releases an excess number of electrons in the vicinity (in the attached wire). In a circuit, charges move because they are repelled from like charges and attracted to unlike charges. ![]() If I do the experiment with a charged balloon, I can use my hand to push the charged object towards another. In this general definition of of electric potential you can imagine any external force you want pushing the charge. (If it accelerates then all sorts of new physics starts to happen involving magnetism, which at the moment is way over our heads.) For now we make our charges sit still (static) or we move them super slow where they move but they don't accelerate, a condition called "pseudo-static". It is important not to push too long or too hard because we don't want the charged particle to accelerate. If you want to actually move a charge, you have to apply an ever-so-slightly greater force to the charge to get it to start moving. In almost all circuits, the second point is provided and this absolute idea isn't needed. It's the same voltage as usual, but with the assumption that the starting point is infinity away. ![]() A common choice that lots of engineers and scientists make is "A is infinity away from the charged object." When we make that choice, we say we are determining the absolute potential energy, or the absolute voltage. If I don't give it to you, you have to make one up. What if I told you where B was but did not mention A? I might say it this way: "What is the potential energy of a test charge when you place it at B"? Well, you need an A to answer that question. There are just a few oddball situations that give us some trouble. To use this equation you have to put in two locations, A and B. For example, you could be moving your test charge towards or away from some charged object. That equation tells you how electric potential energy changes when you move a test charge from point A to point B. Go back to the equation for Electric Potential Energy Difference (AB) in the middle of the section on Electric Potential Energy. Electric potential energy difference A B = ∫ r A r B − q E ⃗ ⋅ d r = q Q 4 π ϵ 0 ( 1 r B − 1 r A ) \displaystyle \text \right ) electric potential energy difference A B = ( 4 π ϵ 0 q Q r B 1 ) − ( 4 π ϵ 0 q Q r A 1 ) start text, e, l, e, c, t, r, i, c, space, p, o, t, e, n, t, i, a, l, space, e, n, e, r, g, y, space, d, i, f, f, e, r, e, n, c, e, end text, start subscript, A, B, end subscript, equals, left parenthesis, start fraction, q, Q, divided by, 4, pi, \epsilon, start subscript, 0, end subscript, end fraction, start fraction, 1, divided by, r, start subscript, B, end subscript, end fraction, right parenthesis, minus, left parenthesis, start fraction, q, Q, divided by, 4, pi, \epsilon, start subscript, 0, end subscript, end fraction, start fraction, 1, divided by, r, start subscript, A, end subscript, end fraction, right parenthesis ![]()
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