Chapter 25, Problem 29SP

What happens to the electric potential at a point in space due to a point charge if that charge is doubled?

To determine

The effect on the electric potential at a point in space due to a point charge if that charge is doubled.

Answer to Problem 29SP

Solution:

D oubled

Explanation of Solution

Introduction:

The absolute potential at a point is the work done against electric forces in carrying a unit positive test charge from infinity to that point.

Explanation:

Consider a point charge q in a vacuum and a point P at a distance r from that point charge. The expression of absolute potential V in vacuum at a point P due to the charge q is,

$V=k_0\frac{q}{r}$…… (1)

Here, $r$ is the distance of the charge from the point and $k_0=8.99\times {10}^9\text{N}\cdot {\text{m}}^{\text{2}}{\text{/C}}^{\text{2}}$

If the charge is doubled, substitute 2 q for q in expression $\left(1\right)$, the expression for absolute potential $V^{\prime }$ at a point P at a distance r from that charge will be,

$V^{\prime }=k_0\frac{\left(2q\right)}{r}$…… (2)

Dividing equation $\left(2\right)$ by $\left(1\right)$,

$\frac{V^{\prime }}{V}=\frac{k_0\frac{\left(2q\right)}{r}}{k_0\frac{q}{r}}$

Simplify:

$\begin{array}{l}\frac{V^{\prime }}{V}=\frac{2}{1}\\ V^{\prime }=2V\end{array}$

Conclusion:

The electric potential at a point is doubled as the charge gets doubled.