How Do Potentials and Test Charges Interact?

[Aphrael]

I have a few general questions which I need some clarification on.

1. What is really the relationship between potentials and test charges? I know how they relate to capacitance, but not really to each other. For example would a charge of 5mC be drawn to a potential of -7V or 7V?

2. I know that two equal charges, like +8 and +8, will cancel each other, but I want to clarify if +6 and -6 cancel as well. I am thinking that they do because they are still of equal force and are in opposite directions, but I just want to make sure.

3. If you have a line with +3 and -3 and you place a charge of -7 between them do they have the same force on the -7 charge, but are both in the same direction because one attracts and one repels? So, for example, if the force from the +3 on the -7 was 2 N, would the combined forces be 4 N to the direction of the +3?

 

[Dick]

For 3) (which makes the most sense), yes, both forces will act in the same direction. The will only have the same magnitude if the -7 charge is the same distance from both of the 3 charges. For 2) opposite charges cancel if they are sitting on top of each other. Otherwise, they still produce an electric field, just as in 3), the field only cancels if you are directly between them. For 1) (which makes the least sense) charges aren't 'drawn to' potentials. They are pulled by electric fields, which are produced by a gradient in potential.

 

[Moetasim]

Potential and test charges are two important concepts in the study of electricity and electromagnetism.

1. The relationship between potentials and test charges can be understood in terms of the concept of electric potential energy. Potential refers to the electric potential energy per unit charge at a specific point in an electric field. Test charges, on the other hand, are imaginary charges used to measure the potential at different points in the field. The potential at a point is directly proportional to the test charge used to measure it. In your example, a charge of 5mC would be drawn to a potential of -7V as they are directly proportional to each other. Higher potential means higher potential energy, so a charge with higher potential will be attracted to a charge with lower potential.

2. Yes, two charges of equal magnitude but opposite sign will cancel each other out. This is because the forces they exert on each other are equal in magnitude but opposite in direction. In the case of +6 and -6, they will also cancel each other out as they have equal magnitude and opposite direction. This is known as the principle of superposition, where the total force on a charge is the vector sum of all the individual forces acting on it.

3. In this scenario, the +3 and -3 charges will still have equal and opposite forces on the -7 charge. However, the direction of the forces will depend on the direction of the electric field at that point. If the electric field is directed towards the positive charge, then the force on the -7 charge will be in the direction of the +3 charge. If the electric field is directed towards the negative charge, then the force on the -7 charge will be in the direction of the -3 charge. The combined force on the -7 charge will be the vector sum of these two forces. So, in your example, if the force from the +3 charge is 2N and the force from the -3 charge is also 2N, then the combined force will be 4N in the direction of the +3 charge. This can also be understood in terms of electric potential, where the potential at the point where the -7 charge is located will be the sum of the potentials due to the +3 and -3 charges.

I hope this clarifies the relationship between potentials and test charges. If you have any further questions, please feel free to ask.