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Derive an expression for the electric potential energy of a system of two point charges in the absence of an external electric field. |
Answer» Solution : Consider the charges `q_(1) and q_(2)`are initially at INFINITY. First, the charge `q_1`is brought from infinity to the point A and no work is done for this. This is because there is no electric field to oppose this charge. Consider another point B at a distance .R. from A. Electric potential at B due to `q_1`is given by `V_(1) = 1 / (4piepsilon_(0))q_(1)/r` Next the charge `q_2`is brought from infinity to the point B. When the charge `q_2`is moved, the electric field due to `q_1`opposes it. Hence work has to be done. Work done in BRINGING the charge `q_2`from infinity to the point B is given by `w=V_1xxq_(2) "" [ :. V=(w)/q_(0)impliesw=q_(0)V]` `w = 1/(4piepsilon_(0))(q_1)/(r)xxq_2` This work done is stored in the charges as potential ENERGY and is given by `PE = 1/(4piepsilon_(0))(q_1q_2)/r` |
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