# Electric Field of a Point Charge

• nezsmith
In summary: The person is trying to solve a problem and the computer is telling them they are wrong. They are trying to get the computer to give them the answer in full significant figures. They are also trying to avoid accumulating rounding error.
nezsmith
[moderators note: moved from technical forum, so no template]

Summary: I can't tell where the mistake in my process is. The computer keeps telling me I am wrong.

The Question:

What is the electric field at point 1 in the figure? Give your answer in component form.(Figure 1)Assume that a = 2.5 cm ,b = 0.70 cm , and q = 4.8 nC .

The formulas:

Electric Field at the point = k|q|/r^2 = E1

E1 as components = E1cos(theta)i + E1sin(theta)j

Theta = arctan(0.025/0.007)= 74 degrees

r1=r3= sqrt(0.025^2+0.007^2) = 0.026 m

The attempt:

8.99e^9|4.8e^-9|/(0.026^2) = 63 834 N/C

E(vector) = 63834cos74i + 63834sin74j

E1x = 1.8 x 10^4 and E1y = 6.1 x 10^4 N/C

Can anyone confirm or deny this answer?

Last edited by a moderator:
Your work looks good to me. However, when you plug in numbers as you go, you run the risk of accumulating "rounding" error. You can avoid this by working out expressions for ##E_x## and ##E_y## symbolically in terms of the given quantities ##q##, ##a## and ##b##. Plug in numbers only at the very end. When I do that, I find that I get a slightly different result to 2 significant figures. If you have a problem where it really is more convenient to calculate as you go, then keep a couple of extra significant figures in the intermediate calculations and round to the proper number of significant figures at the end.

I think it's pretty lousy if the computer grader doesn't allow for some tolerance.

It could be that the computer's answer is just wrong.

vela
I get that both answers are wrong by 1 in the second digit. As TSny suggested, I believe you have just made enough round off or truncation error in intermediate calculations that your answers rounded off the wrong direction from correct. Do the whole calculation at full precision and just round off to the appropriate number of digits at the end.

Thank you to both of you. That would seem to be the case.

There is some room for being off but only if you get the significant digits correct. So if 2.2 is the answer 2.21 or 2.29 may work. In this case I'm off in my significant figures so it won't give me the grade.

In any case, thank you again for the confirmation.

## What is an electric field?

An electric field is a physical quantity that describes the influence that a charged particle exerts on other charged particles in its surrounding space.

## What is a point charge?

A point charge is a concept used in physics to represent an object or particle that has a non-zero electric charge and is considered to be infinitely small in size. This simplifies calculations and allows for easier analysis of the electric field.

## How is the electric field of a point charge calculated?

The electric field of a point charge can be calculated using the formula E = kq/r², where E is the electric field, k is Coulomb's constant, q is the charge of the point charge, and r is the distance between the point charge and the location where the electric field is being measured.

## What is the direction of the electric field of a point charge?

The electric field of a point charge is a vector quantity and its direction is determined by the direction of the force that a positive test charge would experience if placed in that field. The direction of the electric field is away from the positive charge and towards the negative charge.

## How does the electric field of a point charge change with distance?

The electric field of a point charge decreases with distance according to the inverse square law. This means that as the distance from the point charge increases, the electric field strength decreases exponentially. This relationship is described by the formula E ∝ 1/r², where E is the electric field and r is the distance from the point charge.

• Introductory Physics Homework Help
Replies
23
Views
376
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
23
Views
927
• Introductory Physics Homework Help
Replies
3
Views
213
• Introductory Physics Homework Help
Replies
3
Views
948
• Introductory Physics Homework Help
Replies
3
Views
805
• Introductory Physics Homework Help
Replies
5
Views
861
• Introductory Physics Homework Help
Replies
11
Views
2K