How Do You Calculate the Net Electrostatic Force on a Central Charge?

[keemosabi]

Homework Statement

A charge of -3.00 µC is fixed at the center of a compass. Two additional charges are fixed on the circle of the compass (radius = 0.125 m). The charges on the circle are -4.00 µC at the position due north and +5.00 µC at the position due east. What is the magnitude and direction of the net electrostatic force acting on the charge at the center? Specify the direction relative to due east (0°).

http://g.imagehost.org/download/0048/force Click for a bigger image.


I used Couloumb's Law to get the above picture, but what do I do now?

 

[AEM]

Well, you seem to have found the resultant vector. That's the right idea. Don't you have a theorem from geometry that will let you figure its length from the other two? (Hint c^2 = a^2 + b^2)
The angle involves the arctangent.

 

[keemosabi]

Well, you seem to have found the resultant vector. That's the right idea. Don't you have a theorem from geometry that will let you figure its length from the other two? (Hint c^2 = a^2 + b^2)
The angle involves the arctangent.

How do I know the side length of the dotted line? It looks shorter than the 6.912 across from it.

 

[AEM]

How do I know the side length of the dotted line? It looks shorter than the 6.912 across from it.

Well, it seems to me that you have been too sloppy with your diagram. You will have a vector to the right representing the force of the charge to the East on the charge in the center and a vector down representing the force due to the charge to the north. You've computed these values. Make a scale drawing of the vectors and then use the parallelogram law for addition of the vectors. The diagonal of the parallelogram is the resultant. Here your parallelogram will be a rectangle and you can easily figure out its length.