# Maximum potential given a charge

• c1223
In summary, the conversation discusses a homework question involving a charged hollow metal sphere with a radius of 2cm and a breakdown field of 1MV/m in air. The task is to calculate the maximum charge that can be placed on the sphere and the maximum potential on its surface. Using the equation for electric field, the maximum charge is found to be 4.4x10^-8C. To find the potential, the equation for potential is needed, which is V = Q/4πε_0r. This is different from the equation for electric field due to the relationship between Coulomb's force and potential. The final answer for the potential is 20kV.
c1223

## Homework Statement

So the question states that we have a hollow metal sphere of radius 2cm that is charged up. We take the breakdown field of air to be 1MV/m. We are asked to:

a) Calculate the maximum amount of charge which can be placed on the sphere.
b) Calculate the maximum potential on the surface of the sphere.

## Homework Equations

$E = \frac{Q}{4\Piε_{0}r^{2}}$

## The Attempt at a Solution

a) $1\cdot10^{6} = \frac{Q}{4\Piε_{0}0.02^{2}}$
So we get Q as being $4.4\cdot10^{-8}C$​

However, I'm stuck with what to do next to get the potential. I'm not entirely sure I understand the question? Is it the potential between that space on the surface and the center of the sphere?

I know the answer (or at least it is given as 20kV) but I'm not sure how to arrive at that answer.

Cheers

I think I might have cracked it. I realized that I also need the equation for potential which is:

$V = \frac{Q}{4\Piε_{0}r}$

Could someone please explain why it is $r^{2}$ for electric field but $r$ for potential?

You just need to recall how the potential and the field are related to Coulomb's force.

## What is "maximum potential given a charge"?

"Maximum potential given a charge" is a concept in physics that refers to the maximum amount of electrical potential energy that a charged object can have at a specific point in space. It is also known as the electric potential or voltage at that point.

## How is maximum potential given a charge calculated?

The maximum potential given a charge is calculated by dividing the amount of electrical potential energy by the amount of charge. This value is a measure of the strength of the electric field at a particular point in space.

## What factors affect maximum potential given a charge?

The maximum potential given a charge is affected by the amount of electrical charge present, the distance between the charged object and the point in space, and the properties of the medium between them, such as its dielectric constant.

## Why is maximum potential given a charge important in physics?

Maximum potential given a charge is an important concept in physics because it helps us understand and predict the behavior of charged objects in an electric field. It is also essential in many practical applications, such as designing electrical circuits and calculating the energy storage capacity of capacitors.

## How is maximum potential given a charge related to electric potential energy?

Maximum potential given a charge and electric potential energy are directly related. The maximum potential given a charge is the amount of electrical potential energy that a charged object can have at a specific point in space. It represents the potential energy per unit charge at that point in the electric field.

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