The discussion revolves around determining the stability of electrostatic equilibrium for a point charge at the center of a charged ring. Participants explore concepts related to potential energy, electric fields, and the implications of charge signs on stability.
The conversation is ongoing, with participants raising various approaches and questioning assumptions. Some have suggested calculating the electric field and potential in the vicinity of the center, while others are exploring the implications of symmetry and dimensionality in their analysis.
There are mentions of constraints such as the need to assume charge signs and the dimensionality of the problem, with some participants questioning whether to apply 1D or 2D equations in their calculations.
I don't think you were supposed to get into detailed calculations. That's why the question said simply "motivate your answer". You're looking for a good approximation for the force on a particle that is perturbed off centre.Angela G said:
You have examined $$- \frac{\partial^2 V}{\partial z^2} = \frac{1}{\rho} \frac{\partial}{\partial \rho} \left( \rho \frac{\partial V}{\partial \rho} \right )$$ This says that:Angela G said:
I think you already have said the way the ring field acts and you know which way it makes a charge with a small displacement go for each sign of ##q##.Angela G said:
It was used as a starting case, that's all. The possibility of different signs were discussed earlier.PeroK said:
You solved the stability for the ##z## axis above and you know the direction and therefore force in the plane (toward the center for positive ring) and so you know whether it is stable in the plane of the ring given the sign of the charges. If you want to be more detailed for example on the ##z## axis just compute the potential along the ##z## axis which is easy because of symmetry and take the second derivative of it.Angela G said:
Looks correct.Angela G said:
