# Coulomb's Law in 3D: Find Electric Force & Field

• Sofia Matthews
In summary, the problem involves two charges, q1=5 x 10^-6C located at (1,2,-1) and q2=-3 x 10^-6 C located at (-2,1,3). The electric force caused by q2 on q1 can be found using Coulomb's law (F=kq1q2/r^2) and the electric field at (0,0,0) can be calculated using the formula E=F/q. The line of action of the force between the two charges can be found by determining the distance between them.
Sofia Matthews

## Homework Statement

q1= 5 x 10^-6C position (1;2,-1)
q2= -3 x 10^-6 C position (-2,1,3)

a) what is the electric force caused by q2 on q1? (vector notation)
b) what is the electric field at (0,0,0)

F = kq1q2/r^2
E= F/q

## The Attempt at a Solution

I really don't know how to start this problem. Since this problem is in 3D, I don't know how to find the z coordinate of the electric force.

What I initially did was to find the electric force with Coulomb's law, but it gives me a number and not components. I tried to play with Pythagoras's theorem, but didn't figure anything out. [/B]

Last edited:
Welcome to PF!
Sofia Matthews said:
I really don't know how to start this problem.
You need to provide an attempt. It is mandatory while posting in the homework help section.

Sofia Matthews said:
I don't know how to find the z coordinate of the electric force.
In terms of the positions P and Q of two charges, what is the line of action of the force between them?

## 1. What is Coulomb's Law in 3D?

Coulomb's Law in 3D is a mathematical equation that describes the relationship between electric charges and the force they exert on each other in three-dimensional space.

## 2. How is the electric force calculated using Coulomb's Law in 3D?

The electric force between two charged particles in 3D can be calculated by multiplying the product of their charges by the inverse square of the distance between them and the unit vector in the direction of the force. This can be represented by the equation F = (k*q1*q2/r^2) * (r/r), where k is the Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them.

## 3. Can Coulomb's Law in 3D be used to find the electric field?

Yes, Coulomb's Law in 3D can also be used to find the electric field at a specific point in space. The electric field is calculated by dividing the electric force on a test charge by the magnitude of the test charge. This can be represented by the equation E = (k*q1/r^2) * (r/r), where k is the Coulomb's constant, q1 is the charge of the source particle, and r is the distance between the source particle and the point where the electric field is being measured.

## 4. How is Coulomb's Law in 3D different from Coulomb's Law in 2D?

Coulomb's Law in 3D takes into account the three-dimensional nature of space, whereas Coulomb's Law in 2D assumes that all charges are located on a 2D plane. This means that the distance between two charges in 3D is calculated using the three-dimensional distance formula, while in 2D it is calculated using the two-dimensional distance formula.

## 5. What are the units of measurement for the electric force and field in Coulomb's Law in 3D?

The units of measurement for the electric force in Coulomb's Law in 3D are Newtons (N), while the units for the electric field are Newtons per Coulomb (N/C). These units can also be expressed in terms of the fundamental SI units of kilograms (kg), meters (m), and seconds (s).

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