Question

There are infinite number of charges, each equal to ‘q’, which are placed along the X-axis at points x = 1, x = 4, x = 16, x = 64……..Then, determine the electric potential due to this system of charges at the point x = 0.

(a) V=\(\frac {16q}{3\pi \varepsilon_o}\)

(b) V=\(\frac {3q}{4\pi \varepsilon_o}\)

(c) V=\(\frac {4q}{8\pi \varepsilon_o}\)

(d) V=\(\frac {3q}{16\pi \varepsilon_o}\)

I have been asked this question during an internship interview.

This intriguing question originated from Electrostatic Potential due to a System of Charges topic in division Electrostatic Potential and Capacitance of Physics – Class 12

Answer 1

The correct choice is (d) V=\(\frac {3q}{16\pi \varepsilon_o}\)

Easiest explanation: We know electric potential(V) due to charge ‘q’ is V = \(\frac {kq}{r}\).

Electric potential (V) is a scalar quantity, so, the total potential at x = 0 is the sum of all the individual charges

V=[\((\frac {kq}{1}) + (\frac {kq}{4}) + (\frac {kq}{16}) + (\frac {kq}{64}) \) + ……..]

V=kq\((\frac {1}{(1-\frac{1}{4})})\)  → sum of infinite G.P=\(\frac {a}{(1-r)}\)

V=\((\frac {q}{4\pi \varepsilon_o}) \times (\frac {3}{4})\)

V=\(\frac {3q}{16\pi \varepsilon_o}\)