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Question
If an external electric field (E) is applied on the system, write the expression for the total energy of this system.
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Solution
An external field E is applied to the system:
The q1 and q2 are two charges located at r1 and r2 in an external electric field (E).
Work done in bringing q1 from infinity to r1 = W1 = `q_1 V_(r_1)`
Work done on q2 for bringing it from infinity to r2 against the external field (E) = W2 = `q_2 V_(r_2)`
Work done on q2 against the field due to q1 = W2 = `(q_1 q_2)/(4 pi epsilon_0 r_12)` ...[r12 = distance between q1 and q2]
So, the potential energy of the system = W1 + W2 + W12
u = `q_1 V_(r_1) + q_2 V_(r_2) + (q_1 q_2)/(4 pi epsilon_0 r_12)`
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