How to Solve Electrostatics Problems Using Coulomb's Law

[Callisto]

Hi,
I'm seeking help with a couple of problems involving electrostatics.

Q1)Calculate the electric field at the centre of a square 0.1m on a side if one corner is occupied by a charge 0.2micro C, and the other three corners are occupied by the charge of -0.9micro C

Q2) A positive test charge Q is placed at the origin of coordinates, and a charge 6Q is fixed to the x-axis at x=2m, find the location of the place along the x-axis where the electric field due to these is zero.

In Q1 I calculate the forces F12, F13, F14which=F12 using Coulombs Law.
Then taking the vector sum of F12 and F14 and adding F13 gives the electric field at the centre of the square. I'm getting confused with the signs in the equations, what am I doing wrong?

In Q2 I add the to E-fields together and set the sum to zero and solve for x,
ie; E1+E2=kQ/x^2+k6Q/(x+2)^2=0
Is this right, or am I doing something really stupid?
Any help with these problems would be much appreciated, as I've spent sometime on them and I've gotten nowhere.

Thanks Heaps
Callisto

 

[maverick280857]

Use an X-Y frame (axes)

Hint #1 (for both questions): Write the vector components of the force/field in terms of a X-Y reference frame (i, j components), to avoid confusion with the signs.

Hint #2 (for both questions): Before writing the vector sum, write the individual force/field vectors and convince yourself of their directions (as expressed by your equations with what they must be, logically).

Cheers
Vivek

 

[Callisto]

Thanks Vivek,
I've drawn diagrams for both questions.
In Q1 the positive charge experiences an attractive force towards the other charges,
Do i drop the signs in the equations? still unsure.
For Q2 the two charges experience a repulsive force, the two fields must equal zero in between the charges, closer to Q. Still confused.
Thanks

 

[Doc Al]

I'll add a few comments to maverick280857's excellent advice.

In Q1 I calculate the forces F12, F13, F14which=F12 using Coulombs Law.
Then taking the vector sum of F12 and F14 and adding F13 gives the electric field at the centre of the square. I'm getting confused with the signs in the equations, what am I doing wrong?

First off, you should be calculating the contribution each charge makes to the electric field at the center, not the forces between the charges. The electric field from a point charge is: $E = kQ/r^2$. To find the direction of each field contribution, realize that the field from a positive charge points away from the source charge, but the field from a negative charge points towards the source charge. Draw them as vectors and add them using components.

In Q2 I add the to E-fields together and set the sum to zero and solve for x,
ie; E1+E2=kQ/x^2+k6Q/(x+2)^2=0
Is this right, or am I doing something really stupid?

No, it's not right. Realize that for a point between x = 0 and x = 2 the field from each charge points in the opposite direction: E1 points to the right, so E1 = kQ/x^2; E2 points to the left, so E2 = -k6Q/(x+2)^2.

Don't blindly rely on formulas to tell you the direction of the field. Use your knowledge of how the field must point.

 

[Callisto]

Thanks Heaps,Vivek and Doc Al.

Ive had Success!