# Potential due to point charge

## Homework Statement

The electric potential at a distance of 20.5 cm from a very small charged sphere is 33.0 V, with the potential taken to be zero at an infinite distance from the sphere.

If the sphere is treated as a point charge, what is its charge?

## Homework Equations

$$V = \frac {U} {q_{0}} == \frac {1} {4*pi*(8.85*10^{-12})}*\frac {q} {r}$$

## The Attempt at a Solution

How do you convert 33.0V to the correct units of Q or is it equliv?

$$\frac {1} {4*pi*(8.85*10^{-12})}*\frac {33.0} {0.255}$$ ??

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Hootenanny
Staff Emeritus
Gold Member
You don't need to convert your potential into anything, you already have an expression for V, so use it;

$$V = k\cdot\frac{q}{r} \Leftrightarrow q = \frac{V\cdot r}{k}$$

Also note that $20.5 cm \neq 0.255 m$, its probably just a typo.

You don't need to convert your potential into anything, you already have an expression for V, so use it;

$$V = k\cdot\frac{q}{r} \Leftrightarrow q = \frac{V\cdot r}{k}$$

Also note that $20.5 cm \neq 0.255 m$, its probably just a typo.
Thank you, yes that was a typo.