Two parallel plates with area 0.02 m^2, separated by a distance of 0.04 m,genera

Question

Two parallel plates with area 0.02 m^2, separated by a distance of 0.04 m,generate a uniform electric field with magnitude 2*10^4 N/C between them. (use 0= 9*10^-12 C^2/Nm^2)
(i) Calculate the magnitude of the charge on each plate.
(ii) Calculate the force acting on a 30 nC charge positioned half-way between thetwo plates.
(iii) If the 30 nC charge from (ii) moves from half-way between the plates to thepositively charged plate, what is the work done on it by the electric field?
(iv) Is the electric field doing a positive or a negative work on the moving chargefrom (iii)?

Explanation / Answer

i)we know that,

E = V/d => V = E d

V = 2 x 10^4 x 0.04 = 800 V

We know that,

C = epsilon0A/d

C = (8.85 x 10^-12) 0.02/0.04 = 4.43 x 10^-12 F

We know that, Q = CV

Q = 4.43 x 10^-12 x 800 = 3.54 x 10^-9 C

Hence, Q = 3.54 x 10^-9 C = 3.54 nC

ii)We know that, force due to the presence of electric field is:

F = q E

F = 3.54 x 10^-9 x 2 x 10^4 = 7.08 x 10^-5 N

Hence, F = 7.08 x 10^-5 N

iii)we know that, work done is:

W = F x d

W = 7.08 x 10^-5 x 0.04/2 = 1.42 x 10^-6

Hence, W = 1.42 x 10^-6 J

iv)The work done by the electric field is positive.

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