Finding Charge on a Cube Corner

[Cefari]

Homework Statement

Given a cube with equal charges on all corners save one, find the charge on the origin.
http://img79.imageshack.us/img79/4968/cubekg7.jpg

Homework Equations

F = kQ₁Q₂

The Attempt at a Solution

My current idea is splitting up the magnitude of all charges on the origin into their X,Y, and Z components.

Because all magnitudes are formed with right triangles I can use pythagorean theorem to solve for the components and I get:

Q1: +1 in the X
Q2: +1 in the Z
Q3: +1 in the Y
Q4: +1 in the X, Z
Q5: +1 in the X, Y
Q6: +1 in the Y, Z
Q7: +1 in the X, Y, Z

So the sum of the magnitudes acting on the origin would be +4 in all directions, and I have a feeling this is wrong.

 

[tiny-tim]

Hi Cefari!

I don't understand either the question or your answer.

Do you mean find the field at the origin?

If you're adding fields, remember that they're vectors (with a direction), and the strength is 1/distance-squared.

 

[baba89]

Your approach is a good start, but it is missing a key concept in electrostatics - the principle of superposition. This principle states that the net force on a charged particle is the vector sum of all the individual forces acting on it due to other charges. In this case, the charge on the origin will experience a force due to each of the other charges on the corners of the cube.

To find the net force on the origin, you will need to calculate the force due to each individual charge, taking into account the distance between the charges and the direction of the force. This can be done using Coulomb's law, F = kQ1Q2/r^2, where k is the Coulomb's constant, Q1 and Q2 are the charges on the two particles, and r is the distance between them.

Once you have calculated the force due to each individual charge, you can use vector addition to find the net force on the origin. The magnitude of the net force will not necessarily be equal to the sum of the magnitudes of the individual forces, as the forces may cancel out in certain directions.

Once you have found the net force, you can use Newton's second law, F = ma, to find the charge on the origin. Since the charge is at rest, the net force on it must be zero, so you can set the net force equal to zero and solve for the charge.

In summary, your approach was a good start, but you will need to take into account the principle of superposition and use Coulomb's law and vector addition to find the net force on the origin and the charge on it.