Four point charges qA=3 C, qB=-2 C, qC=3 C and qD= -2 C are located at the corne

Question

Four point charges qA=3 C, qB=-2 C, qC=3 C and qD= -2 C are located at the corners of a square ABCD of side 10 cm. * Work individually * All works are required * Make sure you label ABCD in order to represent square corners correctly * All vectors should have directions

a) If you place a charge q=1 C at the center of square, find resultant electric force on center particle?

b) If you place a charge q=1 C at the center of square, what is the electrical potential at the center of the square?

c) If you place a charge q=1 C at the center of square, find the electrical field at the center of the square without center charge?

d) What is the total potential energy of the system without center charge mentioned above?

Explanation / Answer

given

4 point charges on vertices of a square of side a = 0.1 m

qa = 3uC

qb = -2 uC

qc = 3 uC

qd = -2 uC

a. electric field on the center of the square = E

assuming A to be at origin and follow CCW numbering

E = 2k(qa(cos(45)i + sin(45)j) + qb(-cos(45)i + sin(45)j) + qc(-cos(45)i - sin(45)j) + qd(cos(45)i - sin(45)j))/a^2

E = sqrt(2)*k(3(i + j) + 2(i - j) + 3(-i - j) + 2(-i + j))/a^2 = 0

hence net forc eon the particel inthe middle of the square is 0 too

b. at the center of the square, potential = V

now

V = k(qa + qb + qc + qd)*sqrt(2)/a = 0

c. for the center of the square E = 0 V/m

d. without center charge, total PE of the system is

PE = k(qa*qb + qa*qc/sqrt(2) + qa*qd + qb*qc + qb*qd/sqrt(2) + qc*qd)/a

PE = k(13 - 24*sqrt(2))*10^-6/a*sqrt(2) = -1329723.54364282 J

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