electric potential (urgent)

2011-04-22 6:42 pm

My textbook states that :

V = CQ / r, where C = 1/(4 pi e0) (e0 is permittivity)

Can some1 please tell me how does this equation come from?

thanks

更新1:

I haven't learnt calculus... (this is DSE syllabus) My textbook just mentions 'Consider a positive point charge Q. When infinity is taken as zero potential, the electric potential at a position r away from Q is given by ...(the one I stated)

更新2:

Did you mean that if I want to understand the formula (those w/o any proof in the textbook), most probably I will need to know calculus first? thanks

回答 (1)

天同

2011-04-22 8:41 pm

✔ 最佳答案

I suppose V is the potential at a point of distance r from a point charge of magnitude Q.

The potential at a point is defined as the work done by an external force to bring a unit positive charge from infinity to that point.

To put the above statement into mathematics, we have

work done W = integral{ -F.dr}, with the limits of integration from infinity to r
but by Coulomb's Law,
F = C.Q/r^2
hence W = integral{ (-CQ/r^2).dr}
W = -CQ[integral {dr/r^2}] = -CQ[-1/r + 1/infinity] = CQ/r

Because the work done W is numerically equal to the potnetial by definition, thus
V = CQ/r

2011-04-22 23:21:52 補充：
If your texbook doesn't give a proof, I think you need to take it for granted. In fact, this is the drawback of the DSE physics syllabus, students are asked to remember formulae blindly without understanding the physics concept behind. Such kind of approach is not a good science education.

2011-04-24 00:36:46 補充：
Mathematics, including calculus, is only a tool. The most important thing is to understand the relevant physics concept.

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