Electric Field of a Point Charge

[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?

 

[TSny]

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.

 

[Cutter Ketch]

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.

 

[nezsmith]

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.