The figure shows a cross sectional view of three thin square plates of size 2 m

Question

The figure shows a cross sectional view of three thin square plates of size 2 m x 2 m that are parallel to the xy plane, with a separation of 4 cm between adjacent plates. The charges ontheplates,from bottom to top,areQA =20nC,QB =80nC,andQC =-60nC.

a) Is there a region (between the plates, or above or below the plates) where the electric field is zero? If so, where and why? Hint: you don’t need a calculator if you express the charge densities on plates B (nB) and C (nC) in terms of that on plate A (nA)

b) A proton is released from rest midway between plates B and C. How long will it take until it hits a plate (and which one will it hit)? What is its speed when it hits the plate?

Explanation / Answer

Electric field due to thin Charged sheet is E = Q/eoA

EF due to the three on the top of A is Ea + Eb + Ec

there exisst four regions as ( i considered top as A and bottom as C)

above A

in between A and B

in between B and C

and Below C

so

Above net EF will be due to charges

but in between B and C net charge is 80 -60 = 20 nC

so as above shhet A have 20 nC ,net EF betwn thm is zero

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b) Enet due to all the three sheets is Ea + Eb + EC = Ea

E a = Q/eoA = 20*10^-9/(4 * 8.85*10^-12)

Ea = 565 N/C

now use ma = Eq

a = Eq/m for proton

a = 565 * 1.6*10^-19/(1.67 *10^-27)

a = 5.41 *10^10 m/s^2

for S = d/2 = 4cm/2 = 2 cm

use v^2 = 2as

V^2 = 2* 5.41*10^10 * 0.02

V = 4.65 *10^4 m/s

as V = S/t

t = s/V

t = 0.02/(4.65*10^4)

t = 430 ns

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