Calculating the electric field, multiple point charges

[aliaze1]

Homework Statement

What are the strength and direction of the electric field at the position indicated by the dot?

Part A:
Give your answer in terms of the horizontal and vertical components, separated by commas. Take the positive directions to be up and to the right.

Part B:
Specify the strength of the electric field.

Homework Equations

[1/(4πε₀)]*(|q|/r²)

The Attempt at a Solution

[1/(4πε₀)]=9*10⁹

q₁=-5*10^-9
q₂=10*10^-9
q₃=10*10^-9

r₁=0.02m
r₂=0.04m
r₃=√(0.002)=(0.002)^0.5=~0.0447m

E₁={[9*10⁹]*[5*10^-9]}/(0.02m)²
E₂={[9*10⁹]*[10*10^-9]}/(0.04m)²
E₃={[9*10⁹]*[10*10^-9]}/(0.002m)

E₁=112500 j
E₂=56250 i
E₃=45000

E_{3_i}=45000*(0.04/0.0447)=40249 i
E_{3_j}=45000*(0.02/0.0447)=20134 j

Right is positive, therefore:
E₂= -56250 i
E_{3_i}= -40249 i

E_{Total_i}= -56250 + -40249 = -96499 i
E_{Total_j}= 20134 + 112500 = 133534 j

This is coming out as 'incorrect', and therefore I cannot proceed to part 2

Where am I going wrong?

Thanks!

 

[neutrino]

You need to redo E3.

 

[aliaze1]

You need to redo E3.

typo, sorry, E₃ is actually 45000, unless you mean that that is also incorrect

 

[neutrino]

Oh, okay. 45000 is correct.

I just calculated the x-comp. of E3 and it comes out to 40,268.45638, while your answer is off by almost 20 N/C. I think it's a calculation error somewhere.

 

[aliaze1]

Oh, okay. 45000 is correct.

I just calculated the x-comp. of E3 and it comes out to 40,268.45638, while your answer is off by almost 20 N/C. I think it's a calculation error somewhere.

yea idk for some reason my calculator is giving me the 40249.22359..., anyways, is my y-component correct? i have very few attempts left

thanks

 

[neutrino]

If your calculator doesn't work, then you can use Google's.
http://www.google.com/search?q=4500...ls=com.ubuntu:en-US:official&client=firefox-a

Also make sure if your answer needs to be correct up to a certain number of decimal places.

 

[aliaze1]

If your calculator doesn't work, then you can use Google's.
http://www.google.com/search?q=4500...ls=com.ubuntu:en-US:official&client=firefox-a

Also make sure if your answer needs to be correct up to a certain number of decimal places.

So I assume my method was correct?

Thanks, greatly appreciated

 

[aliaze1]

...still isn't working :(

 

[Tools_ink2]

Homework Statement

What are the strength and direction of the electric field at the position indicated by the dot?

Part A:
Give your answer in terms of the horizontal and vertical components, separated by commas. Take the positive directions to be up and to the right.

Part B:
Specify the strength of the electric field.

Homework Equations

[1/(4πε₀)]*(|q|/r²)

The Attempt at a Solution

[1/(4πε₀)]=9*10⁹

q₁=-5*10^-9
q₂=10*10^-9
q₃=10*10^-9

r₁=0.02m
r₂=0.04m
r₃=√(0.002)=(0.002)^0.5=~0.0447m // r3 = 0.4472

E₁={[9*10⁹]*[5*10^-9]}/(0.02m)²
E₂={[9*10⁹]*[10*10^-9]}/(0.04m)²
E₃={[9*10⁹]*[10*10^-9]}/(0.002m)

E₁=112500 j
E₂=56250 i
E₃=45000

E_{3_i}=45000*(0.04/0.0447)=40249 i
E_{3_j}=45000*(0.02/0.0447)=20134 j

Right is positive, therefore:
E₂= -56250 i
E_{3_i}= -40249 i

E_{Total_i}= -56250 + -40249 = -96499 i
E_{Total_j}= 20134 + 112500 = 133534 j

This is coming out as 'incorrect', and therefore I cannot proceed to part 2

Where am I going wrong?

Thanks!

The answer is E(0,0.2) = (-964.15,-922.9) where E(0,0.2) = 1334.7

 

[Tools_ink2]

please correct the value of r3, then everything should fall into place.

 

[Nekura]

I got (-96392,-92272)

your J value is incorrect. your e1 is incorrect. using the correct sign convention, since e1 is a negative charge, it pulls the dot towards it. not away, therefore e1 should be negative since up and right is positive