Find the Direction of Electric Field at X: Test Your Solution

[-EquinoX-]

Homework Statement

http://img382.imageshack.us/img382/4100/coulombko9.jpg

Homework Equations

In the place marked X what is the direction of the electric field?

The Attempt at a Solution

My solution says that it's upward to the right, am I right?

 

[LowlyPion]

I take it this is a square?

Figure first what is the field from the 2 negative charges. By symmetry this will be directed along the diagonal won't it? What is the magnitude then?

Then figure the field from the larger positive charge which is also along the same diagonal.

Which magnitude is larger?

 

[-EquinoX-]

how do you calculate the magnitude of both?

 

[Defennder]

As LowlyPion said, you have to assume it's a square. Denote the sides by say, d. Now you should be able to calculate the magnitude of the E field strength in terms of d using Coulomb's law.

 

[LowlyPion]

how do you calculate the magnitude of both?

That only makes me wonder how you arrived at your solution.

My solution says that it's upward to the right, am I right?

Or was that just a guess? You weren't using Coulomb's Law?

 

[-EquinoX-]

That only makes me wonder how you arrived at your solution.

Or was that just a guess? You weren't using Coulomb's Law?

Well..I know that Coulomb's Law is F = kq1q2/r^2, am I right? The Coulombs law is only used to find magnitude but not directions...

 

[LowlyPion]

Well..I know that Coulomb's Law is F = kq1q2/r^2, am I right? The Coulombs law is only used to find magnitude but not directions...

If there is a force, there is a direction. You've stated the scalar version of the law.

The vector form ...
http://en.wikipedia.org/wiki/Coulomb’s_law#Vector_form

 

[-EquinoX-]

hmm.. I still haven't solved this problem.. I assume that this problem can be solved by simulating of putting a positive charge on the X location and see where the electric field goes.. am I right? one more thing, why would I want to find the magnitude? The question only asks where the direction is at the position marked X

 

[Elbobo]

Oops nevermind. I forgot that the diagonal does complicate things a tiny bit.

X is a positive test charge. Find the magnitude of the diagonal charge and find its components.

Then just set up force equations in the x and y directions.

 

[LowlyPion]

hmm.. I still haven't solved this problem.. I assume that this problem can be solved by simulating of putting a positive charge on the X location and see where the electric field goes.. am I right? one more thing, why would I want to find the magnitude? The question only asks where the direction is at the position marked X

You would want to calculate the magnitude to be certain which direction it is, positive or negative along the diagonal, which through symmetry is what you would easily expect.

Whether you determine the magnitude as a force with a unit test charge or directly as an E field vector it amounts to the same thing.

Consider that you have three vectors.

1 = -kq/a² x-hat
2 = -kq/a² y-hat
3 = +2kq/(a*√2)²*cos45 x-hat + 2kq/(a*√2)²*sin45 y-hat

Now what do the vectors sum to?

 

[-EquinoX-]

I assume that the answer is negative of the diagonal

 

[LowlyPion]

I assume that the answer is negative of the diagonal

Which direction is negative on the diagonal?