Question

Two point charges, +2.10 μC and -7.70 μC, are separated by 3.90 m. What is the electric potential midway between them?

Answer 1

given

charge  $Q_{1}$ = +2.10 $\mu c$

charge $Q_{2}$ = -7.70 $\mu c$

distance between the charges = 3.90 m

now we need to find electric potential midway between the two charges

let the point be point A

the point is at a distance (3.9/2 = 1.95 m) from both the charges (since midway)

we know the electric potential at a point which is at distance 'x' from a point charge q is given by

$V = \frac{1}{4\pi \varepsilon _{0}}\frac{Q}{r}$ joules/coloumb

where Q = charge

r = distance from the charge

The electric potential du to system of point charges is given by sum of potentials due to individual charges

distance of point A from $Q_{1}$ = 1.95 m

distance of point A from $Q_{2}$ = 1.95 m

so total electric potential is given by

  $V = \frac{1}{4\pi \varepsilon _{0}}\frac{2.1 \times 10^{-6}}{1.95}+\frac{1}{4\pi \varepsilon _{0}}\frac{(-7.7) \times 10^{-6}}{1.95}$

=> $V = \frac{10^{-6}}{4\pi \varepsilon _{0} \times 1.95}(2.1-7.7)$

=> $V = \frac{9 \times 10^{9} \times 10^{-6}}{ 1.95}(-5.6)$

=>   $V = 25.846 joules/coloumb$

hence solved , have good day