Question:
deduce the expression for the potential energy of a system of two point charges q1 and q2 brought from infinity to the points r1 and r2 respectively in presence of external electric field E
Answer:
Let, V(r1) and V(r2) be the electric potentials of the field E at the points having position vectors r1 and r2.
Work done in bringing q1 from infinity to r1 against the external field = q1V(r1)
Work done in bringing q2 from infinity to r2 against the external field= q2V(r2)
Work done on q2 against the force exterted by q1 = 1/4πεo.(q1q2/r12)
Here, r12 is the distance between q1 and q2.
So, the total potential energy of the system= The work done in assembling the two charges
U= q1V(r1)+q2V(r2)+1/4πεo.(q1q2/r12)
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