Which of the following expressions gives the total electric potential energy of three…

PHYSICS · Single correct · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Which of the following expressions gives the total electric potential energy

U

of three point charges

q_{1},q_{2},

and

q_{3}

that are separated by the distances

r_{12},\,r_{13},

and

r_{23}

? (

k

is the Coulomb constant.) (a)

U = k\left(\dfrac{q_{1}q_{2}}{r_{12}}+\dfrac{q_{1}q_{3}}{r_{13}}+\dfrac{q_{2}q_{3}}{r_{23}}\right)

(b)

U = \dfrac{k}{2}\left(\dfrac{q_{1}q_{2}}{r_{12}}+\dfrac{q_{1}q_{3}}{r_{13}}+\dfrac{q_{2}q_{3}}{r_{23}}\right)

(c)

U = k\left(\dfrac{q_{1}q_{2}}{r_{12}}+\dfrac{q_{1}q_{3}}{r_{13}}\right)

(d)

U = k\dfrac{(q_{1}+q_{2}+q_{3})^{2}}{r_{12}+r_{13}+r_{23}}