Question

Three point charges are arranged at the corners of a square of side l as shown in the figure. (Figure 1) What is the potential at the fourth corner (point A), taking V=0at a great distance?Give your answer in terms of Q, l, and the appropriate constants.

Answer 1

Given:

Three-point charges are placed at the three corners of the square of side l.

The charges are respectively,

`-2Q,\text{ Q, +3Q}`

To find:

The potential at the fourth corner

Step-by-step explanation:

The distance between the opposite corners is,

`√(2)l`

The potential at any point at a distance r, from a charge q is,

`\begin{gathered} V=(kq)/(r) \\ k=9*10^9\text{ N.m}^2.C^(-2) \end{gathered}`

For the charges in the three corners, the potential at the fourth corner is,

`\begin{gathered} V=k[(-2Q)/(l)+(Q)/(√(2)l)+(3Q)/(l)] \\ =k(-2√(2)Q+Q+3√(2)Q)/(√(2)l) \\ =kQ(1+√(2))/(√(2)l) \end{gathered}`

Hence, the potential at the fourth corner is,

`kQ(1+√(2))/(√(2)l)`