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

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Homework Help Overview

The problem involves calculating the net electrostatic force on a central charge due to two other fixed charges positioned on a circle. The central charge is negative, while one of the peripheral charges is negative and the other is positive. The context is within electrostatics, specifically applying Coulomb's Law and vector addition to determine the resultant force's magnitude and direction.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply Coulomb's Law to find the resultant force but is uncertain about the next steps. Some participants suggest using geometric principles to determine the resultant vector's length and angle, referencing the Pythagorean theorem and arctangent for calculations. There are questions about the accuracy of the diagram and the side lengths involved in the vector representation.

Discussion Status

The discussion is active, with participants providing guidance on using geometric methods for vector addition. There is an exploration of different interpretations regarding the diagram's accuracy and the forces involved, but no consensus has been reached on the final calculations.

Contextual Notes

Participants note potential issues with the diagram's scale and the representation of vectors, which may affect the calculations. The problem is framed within a homework context, implying constraints on the level of assistance that can be provided.

keemosabi
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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?
 
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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.
 
AEM said:
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.
 
keemosabi said:
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.
 

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