Electric field at a point affected by two charges

[pbj_sweg]

Homework Statement

(a) What is the strength of the electric field at the position indicated by the dot?
(b) What is the direction of the electric field at the position indicated by the dot? Specify direction as an angle measured ccw from the positive x-axis.

$Q_{1} = 4.0 C$
$Q_{2} = 9.0 C$

Homework Equations

$$\vec{E} = \frac{Kq}{r^2}$$
$$\text{Pythagorean's Theorem:}~a^2+b^2=c^2$$
$$K = 9\times10^{-9}$$

The Attempt at a Solution

(a) $\vec{E_{1}}$ = effect of $Q_{1}$ on point
$\vec{E_{2}}$ = effect of $Q_{2}$ on point

$\vec{E_{1}} = \frac{KQ_{1}}{r^2} = \frac{K(4~C)}{r^2} = \frac{K(4~C)}{0.05^2} = 1.44\times10^{13} \frac{N}{C}$
$E_{1}\hat{i} = 1.44\times10^{13} \frac{N}{C}$
$E_{1}\hat{j} = 0 ~ \frac{N}{C}$

distance between $Q_{2}~$ and the point was found with Pythagorean's Theorem to be ~0.118 m.
$\vec{E_{2}} = \frac{KQ_{2}}{r^2} = \frac{K(9~C)}{r^2} = \frac{K(9~C)}{0.118^2} = 5.8\times10^{12} \frac{N}{C}$

Breaking $\vec{E_{2}}$ into it's components:
$E_{2}\hat{i} = E_{2}(\sin(\theta)) = 2.596\times10^{12} \frac{N}{C}$
The angle is between the long leg of the triangle and the hypotenuse and was found using tan(0.05/0.1) to get 26.57°.

$E_{2}\hat{j} = E_{2}(\cos(\theta)) = 5.192\times10^{12} \frac{N}{C}$

$E\hat{i} = E_{1}\hat{i} + E_{2}\hat{i} = 1.44\times10^{13} + 2.596\times10^{12} = 1.696\times10^{13}$
$E\hat{j} = E_{1}\hat{j} + E_{2}\hat{j} = 0 + 5.192\times10^{12} = 5.192\times10^{12}$

$| \vec E | = \sqrt{(1.696\times10^{13})^{2}+(5.192\times10^{13})^{2}} = 1.77\times10^{13}$

(b) direction of electric field is $\tan^{-1}\left(\frac{5.192\times10^{12}}{1.696\times10^{13}}\right)$ = 17.01°.

Both parts of the question are incorrect, and I'm 99% sure the second part is incorrect because the components of the electric field on the point are incorrect. Could someone please point out what I've done wrong? Thank you!

 

[Student100]

$$K = 9\times10^{-9}$$

Is this a typo? Or did you use this value?

 

[gneill]

Recalculate your distance value for Q2. You should keep a few extra decimal places in intermediate values such as this distance. This is to prevent rounding/truncation errors from creeping into your significant figures. Only round at the end for your final results.

 

[pbj_sweg]

Is this a typo? Or did you use this value?

Sorry, that's a typo. It's to the 9th power. I used the correct value.

 

[pbj_sweg]

Recalculate your distance value for Q2. You should keep a few extra decimal places in intermediate values such as this distance. This is to prevent rounding/truncation errors from creeping into your significant figures. Only round at the end for your final results.

Correct distance should be 0.1118 meters instead. I got my final answer to be $1.82\times10^{13}$ which is still wrong. I also didn't round until my final answer. Is there something wrong with my method instead?

 

[gneill]

Correct distance should be 0.1118 meters instead. I got my final answer to be $1.82\times10^{13}$ which is still wrong. I also didn't round until my final answer. Is there something wrong with my method instead?

Your result looks good. They may be quibbling about the significant figures though.

Also, what was your angle for the field direction?

 

[pbj_sweg]

Your result looks good. They may be quibbling about the significant figures though.

Also, what was your angle for the field direction?

I initially got an angle of 17.01° but after recalculating, using the picture you provided, I got 63.25°. Both are wrong . The program usually gives some kind of notification if the issue is with sig figs. Frankly, I think my technique is correct, so maybe MasteringPhysics just has the incorrect answer?

 

[gneill]

Your method for calculating the angle was okay. My figure shows the original field contributions by Q1 and Q2, not the net field. I probably should have added that (let me go back and change the figure). The angle should be a bit larger than 17°, but nowhere close to 63°.

 

[pbj_sweg]

Your method for calculating the angle was okay. My figure shows the original field contributions by Q1 and Q2, not the net field. I probably should have added that (let me go back and change the figure). The angle should be a bit larger than 17°, but nowhere close to 63°.

I see. Is there anything else wrong with my calculations? Thank you so much for your help!

 

[gneill]

I don't see any other problems.

 

[pbj_sweg]

I don't see any other problems.

Thank you, seems like the problem is just incorrect.