# Calculate Electric field from two point charges

• mikehibbert
In summary, to calculate the electric field at a given point using two point charges in cartesian coordinates, you can use the equation E=(1/4piE0)(-qr1/r1^3+qr2/r2^3), where r1 and r2 are the distances between the given point and the two charges, respectively. To find these distances, you can use the formula s = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}, where x, y, and z are the coordinates of the two points. Additionally, to account for the vector components in the equation, you can use the magnitude of the vector and its components
mikehibbert
[SOLVED] Calculate Electric field from two point charges

## Homework Statement

Two point charges with q1=2x10^-5 and q2=-4x1-^-3 are located in free space at (1,3,-1) and (-3,1,-2), respectively, in a cartesian coordinate system. Calculate the electric field E at (3,1,-2)

## Homework Equations

E=(1/4piE0)(-qr1/r1^3+qr2/r2^3)

## The Attempt at a Solution

I understand the above equation but am unsure of how to implement it using cartesian coords?

Last edited:
The distance between two points is:

$$s = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$$

how do i use the vector in this part of the equation though?

q1r1/r1^3

the r1 on top is still a vector...

and then i presume for the bottom part i just take the magnitude of r1 and cube it?

Well I've given you the magnitude of the vector so what do you imagine its components to be?

just (x,y,z) surely?

Make that: $((x_1-x_2) \mathbf{\hat{i}}+...)$ etc.

Awesome, thanks!

## 1. How do I calculate the electric field from two point charges?

To calculate the electric field from two point charges, you need to use the electric field formula, which is E = k*q/r^2, where k is the Coulomb's constant, q is the charge of the point charge, and r is the distance between the two charges.

## 2. What is Coulomb's constant?

Coulomb's constant (k) is a proportionality constant in the electric field formula that relates the strength of the electric force between two charged objects to the distance between them and the magnitude of their charges. It is approximately equal to 9 x 10^9 Nm^2/C^2.

## 3. How do I determine the direction of the electric field from two point charges?

The direction of the electric field from two point charges is determined by the direction of the electric force that would act on a positive test charge placed at that point. The direction of the electric field is always away from positive charges and towards negative charges.

## 4. What is the unit of electric field?

The unit of electric field is Newtons per Coulomb (N/C) in the SI (International System of Units) system of measurement. In other systems, it can be expressed as Volts per meter (V/m) or dynes per statcoulomb (dyn/statC).

## 5. Can the electric field from two point charges cancel each other out?

Yes, it is possible for the electric field from two point charges to cancel each other out. This happens when the two charges are equal in magnitude but opposite in sign, and they are placed at equal distances from the point where you are calculating the electric field. In this case, the total electric field at that point would be zero.

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