# Electric Potential (Potential Energy)

• erinec
In summary, the conversation discusses the determination of the distance of closest approach of a proton fired towards a Hg nuclide with an initial speed of 4.0 * 107 m/s. The correct answer is 13.8 fm, which was found using the equation (1/2)mv2 = kqq/r and consistent units. The conversation also includes troubleshooting for incorrect answers and the confirmation of the correct formula used to solve for r.
erinec

## Homework Statement

A proton is fired from far away towards a Hg nuclide.
Determine the distance of closest approach of the proton to the
centre of the nuclide when the initial speed of the proton is
4.0 * 107 m/s.
(Answer: 13.8 fm)

(1/2)mv2 = kqq/r

## The Attempt at a Solution

I plug the numbers straight in and solve for r to get 3.113 * 10^-15, which is totally different from the correct answer above. (For mercury charge, I used 80e since mercury has 80 protons.)

Check each term in your expression. Are you using consistent units? That seems like a likely place for error.

Yes I used consistent units. And still not getting the answer.
I do not know what I am missing.

Well, I just computed it out using the following values:

Mass of proton = 1.67 X 10 ^-27 kg

electronic charge = 1.6 X 10^-19 coul

$$K = \frac{1}{4\pi\epsilon_o}$$ with $$\epsilon_o$$ = 8.85 X 10^-12 farad/meter and the rest as you gave and got the right answer. So put it aside and try it in the morning. It could be a simple calculation error.

Thanks for the reply!
May I ask what formula you are using to solve for the distance?

Well, I just computed it out using the following values:

Mass of proton = 1.67 X 10 ^-27 kg

electronic charge = 1.6 X 10^-19 coul

$$K = \frac{1}{4\pi\epsilon_o}$$ with $$\epsilon_o$$ = 8.85 X 10^-12 farad/meter and the rest as you gave and got the right answer. So put it aside and try it in the morning. It could be a simple calculation error.

erinec said:
Thanks for the reply!
May I ask what formula you are using to solve for the distance?

Sorry for the double post. I used your equation that you posted. After all, it is the correct expression. Since energy is conserved all of the kinetic energy of the particle become potential energy of the particle at its point of closest approach. I solved your equation for r just like you said.

Ah thanks I got the correct answer now.

You're welcome!

## What is electric potential?

Electric potential, also known as potential energy, refers to the amount of work that is required to move an electric charge from one point to another in an electric field.

## How is electric potential measured?

Electric potential is measured in units of volts (V), which is equivalent to joules per coulomb (J/C).

## What is the difference between electric potential and electric potential energy?

Electric potential is a measure of the electric potential energy per unit charge at a specific point in an electric field. Electric potential energy, on the other hand, is the potential energy that a charged particle possesses due to its position in an electric field.

## What is the formula for calculating electric potential?

The formula for electric potential is V = kQ/r, where V is the potential energy, k is Coulomb's constant (9 x 10^9 Nm^2/C^2), Q is the charge, and r is the distance between the charge and the point where the potential is being measured.

## How is electric potential related to electric potential energy?

Electric potential energy is directly proportional to electric potential. This means that as electric potential increases, so does electric potential energy. In other words, the higher the electric potential, the greater the potential energy of a charged particle in that field.

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