Four particles, each carrying a charge of magnitude 8.0 nC , are at the corners

Question

Four particles, each carrying a charge of magnitude 8.0 nC , are at the corners of a square that has a side length of 3.0 m.

For zero potential set at infinity, calculate the potential at the center of the square if all particles are positively charged.

For zero potential set at infinity, calculate the potential at the center of the square if three particles are positively charged and one is negatively charged.

For zero potential set at infinity, calculate the potential at the center of the square if two particles are positively charged and two are negatively charged.

Explanation / Answer

Here ,

magnitude of charge , q = 8 nC

side , a = 3 m

distance of charges from centre , d = 3/sqrt(2)

d = 3/sqrt(2) = 2.121 m

for the all positive charges

potential at the centre = 4 * k * q/d

potential at the centre = 4 * 9 *10^9 * 8 *10^-9/2.121

potential at the centre = 135.8 V

the potential at the centre is 135.8 V

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if one particle is negatively charged

potential at the centre = (3 -1) * k * q/d

potential at the centre = 2 * 9 *10^9 * 8 *10^-9/2.121

potential at the centre = 67.9 V

the potential at the centre is 67.9 V

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for two postive particles

potential at the centre = (2 - 2) * k * q/d

potential at the centre = 0 * 9 *10^9 * 8 *10^-9/2.121

potential at the centre = 0 V

the potential at the centre is 0 V

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