# An electron is placed at Point P, Calculate the Potential Energy

#### aaika

Problem Statement
An electron is placed at point P.
Calculate the electric potential energy of the electron in units of Joules
Relevant Equations
Net Force = 200.97N
Net Electric Field = 2.51e6N/C
Electric Potential at point P = 5.43e6V

Ub-Ua = -qEd
Change in U = -qEd if F is parallel to d Not quite sure how to approach this question - do I need to calculate -qEd for all three charges and then the electron and add them together?
Thanks

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#### gneill

Mentor
Hi @aaika,

Welcome to Physics Forums!

You're relevant equations look more like given data that would belong in the problem statement.

The Net Force looks suspiciously large. 200 N applied to an electron by an electric field would imply an amazingly large electric field, much larger than what you've specified as the net electric field.

Are you certain that the problem statement is complete and presented exactly as you received it?

#### aaika

Hi @aaika,

Welcome to Physics Forums!

You're relevant equations look more like given data that would belong in the problem statement.

The Net Force looks suspiciously large. 200 N applied to an electron by an electric field would imply an amazingly large electric field, much larger than what you've specified as the net electric field.

Are you certain that the problem statement is complete and presented exactly as you received it?
Thank you :)
Absolutely certain. The three numbers I provided are the correct answers for the previous questions leading to this one. I have directly copy + pasted the problem so there is no missing information.

#### gneill

Mentor
But if we take your net electric field value, 2.51e 6N/C, and insert the charge of an electron in the equation $F = qE$, we arrive at a force value of only about $4.0 \times 10^{-13} \text{N}$. This contradicts your net force value by a rather large margin. Is the force force value you've given really the force on the electron?

#### aaika  Attached are screenshots of the answers being marked as correct.

#### gneill

Mentor
Your original problem statement did not indicate that the given values for Net Force and Net Electric Field pertained to other bodies than the electron. How were we to guess? You should always provide the complete problem statement as given.

#### gneill

Mentor
You have the electric potential at point P. It's units are Volts, which is not a fundamental unit. It is synthesized from Joules/Coulomb ($Volt = \frac{Joule}{Coulomb}$). How do you think you might arrive at the electric potential energy of the electron located at that point?

#### ZapperZ

Staff Emeritus
Science Advisor
Education Advisor
2018 Award
Problem Statement: An electron is placed at point P.
Calculate the electric potential energy of the electron in units of Joules
Relevant Equations: Net Force = 200.97N
Net Electric Field = 2.51e6N/C
Electric Potential at point P = 5.43e6V

Ub-Ua = -qEd
Change in U = -qEd if F is parallel to d

View attachment 243768
Not quite sure how to approach this question - do I need to calculate -qEd for all three charges and then the electron and add them together?
Thanks
The potential energy at any point in space is the product of the "test charge" and the value of the potential at that location, i.e.

U = qV

based on the situation where V at r→∞ is zero.

For the situation where you only have 3 charges as the source charges of the potential field, then the potential potential energy at point P is the work done in moving the electron from very far away (∞) to the point P, i.e. ΔU = U(at p) - U(∞) = U(at p).

Since q = -e and V is given in your problem, this should be straightforward. But you have to have a conceptual understanding of what I described above, because this question can come in a million different varieties.

Zz.

#### aaika

Your original problem statement did not indicate that the given values for Net Force and Net Electric Field pertained to other bodies than the electron. How were we to guess? You should always provide the complete problem statement as given.
My bad - I thought I included that it was relevant to Q3 when I pasted it.

The potential energy at any point in space is the product of the "test charge" and the value of the potential at that location, i.e.

U = qV

based on the situation where V at r→∞ is zero.

For the situation where you only have 3 charges as the source charges of the potential field, then the potential potential energy at point P is the work done in moving the electron from very far away (∞) to the point P, i.e. ΔU = U(at p) - U(∞) = U(at p).

Since q = -e and V is given in your problem, this should be straightforward. But you have to have a conceptual understanding of what I described above, because this question can come in a million different varieties.

Zz.
Thank you for clarifying! I was caught up in the fact that I had Q1-3 as well as an electron and didn't know whether or not those three Q's would be influential in the formulae to figure it out.

U=qV= (-1.60e-19)(5.43e6) = -8.69e-13J which was correct.

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