electric potential

2011-09-26 5:37 am

The radius of the dome of a Van de Graaff generator is 20cm. If air breaks down in an electric field of 3x10^6 NC^-1
Q:what is the highest possible potential of the dome?

更新1:

Can I use V=Ed to find V?

回答 (1)

天同

2011-09-26 5:58 am

✔ 最佳答案

Assume the dome is a perfect sphere. Use the equation: E = kQ/R^2
where k is a contant, equals to 9x10^9 F/m
Q is the charge on the dome with radius R

Hence, 3 x 10^6 = (9x10^9).Q/(20/100)^2
Q = 1.33 x 10^-5 C

Potential of the dome = (9x10^9) x (1.33x10^-5)/(0.2) v = 6 x10^5 v = 600 kV

2011-09-26 20:06:19 補充：
Q:Can I use V=Ed to find V?
A: This is just a special case of E=-dV/dx when the electric field is uniform. But the electric field here doesn't satisfy such criterion.

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