So confused on 7 and 8 please help! Three point charges q_1, q_2, and q_3 are si

Question

So confused on 7 and 8 please help!

Three point charges q_1, q_2, and q_3 are situated at three corners of a rectangle as shown in the diagram below. Here q_1 = +9.00 mu C, q_2 = -9.00 mu C, q_3 = +3.00 mu C. What is the electric potential at the free corner where there is no charge? What charge should be placed at the free corner for the electric potential at the center of the rectangle to be zero? Include both magnitude and sign if applicable. A large capacitance of 1.08 mF is needed for a certain application. Calculate the area the parallel plates of such a capacitor must have if they are separated by 4.81 pm of Teflon, which has a dielectric constant of 2.1. What is the maximum voltage that can be applied if the dielectric strength for Teflon is 60 Times 10^6 V/m Find the maximum charge that can be stored. Calculate the volume of Teflon alone in the capacitor.

Explanation / Answer

here,

q1 = 9* 10^-6 C

q2 = - 9 * 10^-6 C

q3 = 3 * 10^-6 C

(a)

the electric potential at the free corner , V = k * ( q1/0.025 + q3/0.05 + q2 /0.06 )

V = 9 * 10^9 * 10^-6 * ( 9/0.025 + 3/0.05 - 9 /0.06)

V = 2.43 * 10^6 V

(b)

let the fourth charge be q4

the electric potential at the centre , V = k/0.03 * ( q1 + q2 + q3 + q4)

for the potential at center to be zero

0 = ( 9 * 10^-6 - 9 * 10^-6 + 3*10^-6 + q4)

q4 = - 3 * 10^-6 C

q4 = - 3 uC

8)

a)

Capacitance , C = 0.00108 F

d = 4.81 * 10^-6 m

dielectric constant , k = 2.1

let the area be A

epsilon * A /d = C

8.85 * 10^-12 * A /( 4.81 * 10^-6) = 0.00108

A = 586.98 m^2

(b)

let the potential be V

V /d = E

V /( 4.81 * 10^-6) = 60 * 10^6

V = 288.6 V

the maximum voltage applied is 288.6 V

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