A point charge is at the origin (0, 0) on a coordinate system. A point charge q_

Question

A point charge is at the origin (0, 0) on a coordinate system. A point charge q_2 = 3.0 muC is on the X-axis at (3.0, 0) meters. a) If the electric potential is taken to be zero at infinity, find the total electric potential due to these charges at point P, with the coordinates (0, 4.0) meters. b) How much work is required to bring a third point charge of 4.0 mu C from infinity to P? Show that the amount of work required to assemble four identical point charges of magnitude Q at the corners of a square of a side s is 5.41 K_eQ^2/S.

Explanation / Answer

2. magnitude of Point charge is not given that is required.

3. Electric potential energy of two point charge system is given as ,

PE = k q1 q2 / r

for adjacent charges.

PE = k Q Q / s = k Q^2 / s

there 4 sets of this kind.

PE1 = 4 k Q^2 / s

now for diagonal charge set and there are two such sets.

PE2 = 2[ k Q Q / sqrt(a^2 + a^2)] = 1.41 k Q^2 / s

total PE of system = PE1 + PE2 = 5.41 k Q^2 / s

Work done to assemble = PE of system = 5.41 k Q^2 / s

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