# Electric Field Calculation given three point charges?

• P1nkButt3rflys
In summary, the conversation discusses the calculation of the electric field and force between three point charges located in an equilateral triangle. The first part involves calculating the electric field at the location of q3, while the second part involves finding the force on q3. The correct calculations are found using the formula for electric field and the definition of electric force.
P1nkButt3rflys

## Homework Statement

Three point charges are located in an equilateral triangle with side 0.330 cm, where q1 = +8.30 µC, q2 = −8.20 µC, and q3 = +1.90 nC.

A) What is the electric field at the location of q3? Enter the x component, then the y component.

B) What is the force on q3? Enter the x component, then the y component.

DIAGRAM:
http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype51/threechrg1.gif

## Homework Equations

|Fe|= (k*|q1|*|q2|)/r^2
|E|=(k*|Q|)/r^2

k = 8.99*10^9 (N*m^2)/C^2
Fe = Electrostatic force between a pair of charges
r = charge separation
q1, q2 = charge magnitudes
E = electric field
Q = charged object

## The Attempt at a Solution

I've attempted this many ways and have been incorrect each time. I know the angles at the three points of the triangle will be 60deg. Knowing this and that the sides of the triangle are 0.330cm in length I calculated "r" -> the distance in respect to X and Y from q1 to q3 and from q2 to q3.

I got r(1-3x) = 0.165cm and r(1-3y) = 0.286cm and r(2-3x) = 0.165cm and r(2-3y) = 0.286cm.

Any help would be greatly appreciated. Even to just the first portion would help a lot.

Last edited:
Careful -- to calculate the components of the force, you can't use the components of the separation. This is a pretty common mistake, I think, and not very intuitive, but you have to calculate the field vector using the full separation between the charges, and then find the components from that vector.

The difference comes from the formula for electric field. Say for finding the y component of the field, using just the y component of the separation looks like this:
$$E_{y} = k\frac{q_{1}q_{2}}{(rsin\theta)^{2}}$$
Whereas finding the component of the whole field vector looks like this:
$$E_{y} = k\frac{q_{1}q_{2}}{r^{2}}sin\theta$$

1 person
Hi jackarms! Thanks for the help but I'm still very confused. I attempted another solution, again it's wrong.. I'll post my attempt and maybe someone can give me some guidance. I'm not sure if I'm on the right track or completely off in the wrong direction.

[IMAGE REMOVED]

Thank you!

Last edited:
So not only did I use some wrong values in my previous calculation, after reading through my textbook further I approached it differently and got the correct answer for Part A :)

I'm not sure what to do for Part B, but am going to attempt it and post my work.

Attempted B, to find the force on q3 and it is incorrect.

Any suggestions:

All the calculations look right for both the field and the force, so I think one must be wrong. For the field, I'm not sure about the 7.15 x 107 value - are you sure that's right?

Also, an easy way to go from field to force is to just use the definition of field: $E = \frac{F}{q}$
It's just nice to save some work.

1 person
Thanks for the suggestion! I used your equation and got the same result, well, almost. The force for x was the same, the force for y was 0.134 N, so I must have had an issue with my sig figs. I entered both answers and they are correct!

## 1. What is an electric field?

The electric field is a physical quantity that describes the influence that an electric charge has on other charges in its vicinity. It is represented by a vector and is measured in units of newtons per coulomb (N/C).

## 2. How is the electric field calculated?

The electric field at a point in space is calculated by dividing the force on a test charge placed at that point by the magnitude of the test charge. It can also be calculated by using Coulomb's Law, which states that the electric field is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them.

## 3. What are point charges?

Point charges are idealized charges that have a negligible size and are concentrated at a single point in space. They are often used in calculations involving electric fields because they simplify the mathematical equations.

## 4. Can the electric field be negative?

Yes, the electric field can be negative. This indicates that the force on a positive test charge would be in the opposite direction of the electric field vector. It is important to note that the electric field itself is a vector and can have both magnitude and direction.

## 5. How are three point charges taken into account when calculating the electric field?

In order to calculate the electric field given three point charges, you must first determine the individual electric fields for each charge and then use vector addition to find the total electric field at a specific point. This can be done by breaking down the electric field vectors into their x and y components and then adding them together.

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