Question

Eight charges are placed at the vertices of regular cube

Answer 1

Step-by-step explanation:

this question we will calculate the work done in bringing the charges( each 'q') at each corner of cube. which will be equal to the electrostatic potential energy of the system.

So now we can see from fig below,

WA = 0 [ because initially there is no charge]

Now, WB = q.VBA = (q/ 4πϵo) .q

Now, WC = q24π∈o[1a2√ + 1a]

Similarly we can calculate ,WD,WE,WF,WG,WH

Than we will have Wnet = WA+WB+WC+WD+WE+WF+WG+WH

⇒Wnet =q24π∈o[12a+12a2√+4a3√] = 12 ×q24π∈o[1a+1a2√+1a33√] ...........(1)As given in the question, potential energy, U = 12 ×14π∈oq2a×x ...........(2)Compairing (1) &(2) we get, x = [1+12√+133√]

Hence option (4) is the correct answer.

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