Calculating Electric Field Due to Multiple Charged Balls

In summary, the conversation was about determining the electric field at the location of Q1, due to Q2. The formula used was E = q1q2\hat{r} / 4\pi\varepsilon r^2, where q1 and q2 represent the charges of the particles and r is the distance between them. The result was <0, 1.18125e-4, 0>, which was later confirmed to be correct by using Coulomb's law and Coulomb's constant, k.
  • #1
cowmoo32
122
0

Homework Statement


13-46.jpg

At a particular moment, three small charged balls, one negative and two positive,are located as shown in Figure 13.46. Q1 = 3 nC, Q2 = 7 nC, and Q3 = -6 nC.

What is the electric field at the location of Q1, due to Q2?


Homework Equations


[tex]\vec E = q1q2\hat{r} / 4\pi\varepsilon r^2[/tex]


The Attempt at a Solution



r = <0, .04, 0> m
rmag = .04
rhat = <0, 1, 0>

E = [3e-9(7e-9)(9e9)] / .0016

Which gives me:

E = <0, 1.18125e-4, 0>

What am I doing wrong here? At first I figured I missed a negative, so I tried making my answer negative, but apparently that's not the case.
 
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  • #2
cowmoo32 said:
[tex]\vec E = q1q2\hat{r} / 4\pi\varepsilon r^2[/tex]


The Attempt at a Solution



r = <0, .04, 0> m
rmag = .04
rhat = <0, 1, 0>

E = [3e-9(7e-9)(9e9)] / .0016

Which gives me:

E = <0, 1.18125e-4, 0>

What am I doing wrong here? At first I figured I missed a negative, so I tried making my answer negative, but apparently that's not the case.

Isn't the electric field at Q1 due to Q2 given by
E = kQ/r2 = kQ2/(.04)2 ?
 
  • #3
The way we've been doing it in class is the way I posted. We haven't even used k...what does it represent?
 
  • #4
cowmoo32 said:
[tex]\vec E = q1q2\hat{r} / 4\pi\varepsilon r^2[/tex]

Hi cowmoo32! :smile:

No, that's Coulomb's law for the force

the field is just [tex]q2\hat{r} / 4\pi\varepsilon r^2[/tex] :smile:

(I think LowlyPion is saying the same thing, and his k is your [itex]1/ 4\pi\varepsilon[/itex])
 
  • #5
cowmoo32 said:
The way we've been doing it in class is the way I posted. We haven't even used k...what does it represent?

k is Coulomb's constant

[tex]k = \frac{1}{4 \pi \epsilon_0}[/tex]

Edit: Tiny-Tim beat me to it.
 
  • #6
I wrote it as k because Tex is more awkward to pound out.

Sorry if I confused you.
 
  • #7
Thanks for the help, guys.
 

1. What is an electric field?

An electric field is a region in space around a charged object where other charged objects experience a force. It is represented by lines of force that indicate the direction and strength of the electric field.

2. How is the location of an electric field determined?

The location of an electric field is determined by the position and magnitude of the charged object creating the field. The closer the charged object is to another object, the stronger the electric field will be at that location.

3. What factors affect the strength of an electric field at a certain location?

The strength of an electric field at a certain location is affected by the magnitude of the charged object creating the field, the distance from the charged object, and the type of material surrounding the charged object.

4. How can I find the direction of an electric field at a specific location?

The direction of an electric field at a specific location can be determined by the direction of the electric field lines. The direction of the lines of force points towards the direction of the force that a positive test charge would experience if placed in the field.

5. What are some real-world applications of electric fields?

Electric fields have many real-world applications, such as in electronics, where they are used to control the flow of electricity in circuits. They are also used in medical imaging technology, such as X-rays and MRI scans, and in particle accelerators for scientific research.

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