What do you understand by electric potential energy of a system of point charges? Derive the formula for the electric potential energy of the system of three point charges shown in the following figure.
![three point charges q1, q2, q3 at the vertices of a triangle with sides r12

Question

What do you understand by electric potential energy of a system of point charges? Derive the formula for the electric potential energy of the system of three point charges shown in the following figure.
![three point charges q1, q2, q3 at the vertices of a triangle with sides r12, r13, r23 — Class 12 Physics electrostatics question](/figures/electrostatic-potential-and-capacitance/three-charge-triangle-q3-q2-q1-r23-r13-r12-fig-pyq-w721ib.svg)

OR

What is a capacitor? Deduce the formula for the capacity of a parallel plate capacitor in the following conditions -
(i) When the medium between the plates of the capacitor is vacuum.
(ii) When the medium between the plates of the capacitor is a dielectric of dielectric constant K.
(iii) When the medium between the plates of the capacitor is some metal.

Accepted Answer

>

> [!TLDR]
> Electric PE of a charge system is the work needed to assemble the charges from infinity; for a parallel plate capacitor, inserting a dielectric or conductor changes the effective field/gap and hence the capacitance.
>
> **Main question:**
>
> The electric potential energy of a system of point charges is defined as the total work done in assembling the charges at their given positions, by bringing them one by one from infinity (where they are infinitely far apart and non-interacting), against the electrostatic forces of the charges already placed.
>
> **Derivation for three charges $q_1, q_2, q_3$** (separations $r_{12}, r_{13}, r_{23}$ as shown):
>
> - Bring $q_1$ from infinity to its position: no other charge present yet, so $W_1 = 0$.
> - Bring $q_2$ from infinity to its position (distance $r_{12}$ from $q_1$): $W_2 = \dfrac{1}{4\pi\epsilon_0}\dfrac{q_1q_2}{r_{12}}$
> - Bring $q_3$ from infinity to its position (distance $r_{13}$ from $q_1$ and $r_{23}$ from $q_2$): $W_3 = \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1q_3}{r_{13}}+\dfrac{q_2q_3}{r_{23}}\right)$
>
> Total potential energy: $U = W_1+W_2+W_3 = \dfrac{1}{4\pi\epsilon_0}\left[\dfrac{q_1q_2}{r_{12}}+\dfrac{q_2q_3}{r_{23}}+\dfrac{q_1q_3}{r_{13}}\right]$
>
> **OR -- Parallel plate capacitor:**
>
> A capacitor is a device consisting of two conductors (plates) separated by an insulating medium, used to store electric charge and energy; its capacitance is $C = Q/V$.
>
> (i) **Vacuum between plates:** For plate area $A$ and separation $d$, uniform field between plates $E_0 = \sigma/\epsilon_0 = Q/(A\epsilon_0)$, so $V = E_0 d = Qd/(A\epsilon_0)$, giving $C_0 = Q/V = \epsilon_0 A/d$.
> …

Q.What do you understand by electric potential energy of a system of point charges? Derive the formula for the electric potential energy of the system of three point charges shown in the following figure.

Concept understanding — Electrostatic Potential Energy of a System of Charges

Q.What do you understand by electric potential energy of a system of point charges? Derive the formula for the electric potential energy of the system of three point charges shown in the following figure.

Concept understanding — Electrostatic Potential Energy of a System of Charges

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