9. It is possible to make lightning at home. Dry air breaks down if there is a l

Question

9. It is possible to make lightning at home. Dry air breaks down if there is a large enough electric field. The electric field required to break down dry air and cause lightning is 3.0 × 106 V/m.

a) How much charge would you have to put on each plate of a parallel plate capacitor to have a field this large? Assume that the plates have an area of A = 75cm2 and the plates are separated by 1mm.

b) Does the distance separating the two plates matter? If no, why not? If yes, how would the charge required change if you doubled the distance separating the two plates?

c) How much energy is stored in this capacitor?

10. A current of 2mA flows for 1 hour. How much charge flows past one point in a wire during this time? How many electrons is this equivalent to?

Explanation / Answer

9.A. Electric field = V/d

V = E*d = 3*10^6*10^-3 = 3000 V

Capacitance will be

C = e0*A/d

A = 75 cm^2 = 75*10^-4 m^2

d = 1 mm = 10^-3

C = 8.85*10^-12*75*10^-4/10^-3

C = 66.37*10^-12 F

Now

Q = CV

Q = 66.37*10^-12*3000

Q = 199.11*10^-9 C

B. from above equations:

V = E*d

C = eo*A/d

Q = CV = (e0*A/d)*E*d

Q = e0*A*E

so you can see that charge does not depend on distance between the plates.

So if you doublr the distance charge will not change.

C.

U = 0.5*CV^2

U = 0.5*66.37*10^-12*3000^2

U = 2.98*10^4 J

10.

A. I = dq/dt

dq = i*dt

i = 2 mA = 2*10^-3 Amp.

t = 1 hr = 60*60 sec = 3600 sec

dq = 2*10^-3*3600 = 7.2 C

B. q = ne

n = q/e = 7.2/(1.6*10^-19) = 4.5*10^19 electrons.

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