Question

The figure shows 3 point charges at the corners of a rectangle. The top left corner is positive 10nC and the bottom left corner is 5 nC they are both positive. The top side is 3cm while the right side is 4cm the bottom and the left sides are also the same. The top right corner is -10 nC. A -15nC charge is placed at the emply corner that being the bottom right.

A) find the electric potential at the center of the rectangle

B) find the electric potential energy of the configuration.

Answer 1

here,

distance of charges from the centre , r = 2.5 cm

r = 0.025 m

Q1 = 10 nC

Q1 = 10 * 10^-9 C

Q2 = 5 nC

Q2 = 5 * 10^-9 C

Q3 = -15 nC

Q3 = - 15 * 10^-9 C

Q4 = - 10 nC

Q4 = - 10 * 10^-9 C

(a)

the electric potential at the center of the rectangle , V = k *Q1/r + k *Q2/r + k *Q3/r +k *Q4/r

V = 9 * 10^9 * 10 * 10 ^-9/0.025 + 9 * 10^9 * 5 * 10 ^-9/0.025 - 9 * 10^9 * 15 * 10 ^-9/0.025 - 9 * 10^9 * 10 * 10 ^-9/0.025

V = - 3600 V

the electric potential at the center of the rectangle is -3600 V

(b)

the electric potential energy of the configuration is U

U = k * (*Q2/4 + Q1 *Q3 / 5 + Q1 * Q4 / 3 + Q2 * Q4 / 5 + Q2 * Q3/3 + Q3 * Q4 /4)

U = 9 * 10^9 * (( 10 * 10^-9)*( 5 * 10^-9)/4 - ( 10 * 10^-9) *( 15 * 10^-9) / 5 - ( 10 * 10^-9) * ( 10 * 10^-9) / 3 - ( 5 * 10^-9) * ( 10 * 10^-9) / 5 - ( 5 * 10^-9) * ( 15 * 10^-9)/3 + (15 * 10^-9) * ( 10 * 10^-9) /4))

U = - 4.35 * 10^-7 J

the electric potential energy of the configuration is - 4.35 * 10^-7 J