Physics Electrostatic Potential

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Electrostatic Potential

Electric potential energy between two point charges

Consider two charges Q and q separated by a distance `r_1,` If the charge q is moved along the line joining the charge and the final separation becomes `r_2` , then the work done by the electric force during the process is

`W = int_(r_1)^(r_2) (kQq) /r^2 = kQq[1/r_1 - 1/r_2]`

The change in potential energy is defined as

`U_2 - U_1 = -W = kQq[1/r_1 - 1/r_2]`

The potential energy of a two-charge system is taken to be zero, when the distance between the charges is infinity. i.e. `U = 0` if `r =oo`
Now, the potential energy of a two charge system when their separation is r, is

`U(r) -0 = kQq[1/r_1 - 1/oo]`

`U(r) = (kQr)/r = 1/(4piepsilon_0) (Qq)/r`

For like charges U is +ve & for unlike charges U is-ve.

Electric potential energy between more than two point charges

The above equation gives the potential energy of a pair of charges.ln case of three charges (say `q_1 , q_2`
and q) there arc three pairs `(q_1, q_2) ,` `(q_2, q_3)` and `(q_3, q)` Thus the total potential energy of the system
will have three terms.

`U = (kq_1q_2)/r_(12) + (kq_2q_3)/r_(23) + (kq_3q_1)/r_(31)`