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प्रश्न
Answer the following question.
If an external electric field (E) is applied on the system, write the expression for the total energy of this system.
उत्तर
Let us consider a system of two charges q1 and q2 located at a distance r1 and r2 from the origin. Let these charges be placed in an external field of magnitude E. Let the work done in bringing the charge q1 from infinity to r1 be given as q1V(r1) and the work done in bringing the charge q2 from infinity to r2 against the external field can be given as q2V(r2). We note that, in the latter case, the work required to be done on q2 will include the field due to the charge q1 along with the electric field E, which can be given as,
`= (Kq_1q_2)/(r_12)`
The potential energy of the point q at a distance r from the origin in an external electric field is given as qV(r).
Where V(r) is the external potential at that point.
Here, r12 is the distance between q1 and q2. we can add these two to get the total work done in bringing q2 from infinity to r2
= `q_2V(r_2)+(Kq_1q_2)/(r_12)`
Thus, the total work done required to bring both the charges from infinity to the present configuration or the total potential energy of the system can be given as
`= q_1V(r_1)+q_2V(r_2) + (Kq_1q_2)/(r_12)`.
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