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Obtain the equation of electric potential energy of a system of two electric charges in external electric field. |
Answer» Solution :Two electric charges `q_(1)` and `q_(2)` are brought from INFINITY distance through distance `r_(1)` and `r_(2)` relative to origin in external electric field. The work done in bringing the charge `q_(1)`, from infinity through `r_(1)`, distance, `W_(1)=q_(1)V(vecr_(1))` and work done in bringing `q_(2)` through distance `r_(2)` . Here work is done not only against the external field `vecE` but also against the field due to `q_(1)` `W_(2) = q_(2)V(vecr_(2))` Work done on `q_(2)` against the field due to `q_(1)`. `W_(3)=(kq_(1)q_(2))/(r_(12))` where `r_(12)` is the distance between `q_(1)` and `q_(2)` The total potential energy of the system = the total work done in ASSEMBLING the configuration or potential energy `U=q_(1)V(vecr_(1))+q_(2)V(vecr_(2))+(kq_(1)q_(2))/(r_(12))` |
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