Cavity in Sphere: What Happens with a Third Charge?

[heman]

I am thinking over this,
there are two spherical cavities in the interior of a neutral conducting sphere.the cavities have point charges qA and qB respectively at their centres.
What will happen when we bring a third charge near the sphere...

 

[reilly]

It all depends, particularly on the relative sign of the charges, and whether they are held in place by non-electromagnetic forces. It's all about forces and constraints.

Regards,
Reilly Atkinson

 

[GSXR750]

When a third charge is brought near the sphere, the charges in the cavities will experience a force due to the presence of this third charge. Depending on the magnitude and sign of the third charge, the charges in the cavities may either be attracted or repelled. This will cause a redistribution of charges within the sphere, as the charges in the cavities will try to align themselves with the third charge in order to minimize the overall potential energy of the system.

If the third charge is positive, the charges in the cavities will be attracted towards it and the overall charge distribution in the sphere will become asymmetric. This will result in a net electric field inside the sphere, as the charges in the cavities will no longer cancel each other out. If the third charge is negative, the charges in the cavities will be repelled and the overall charge distribution in the sphere will remain symmetric, resulting in no net electric field inside the sphere.

In either case, the presence of the third charge will affect the electric potential within the sphere and may also cause a shift in the location of the centre of charge. This can be calculated using the formula for electric potential, V = kq/r, where k is the Coulomb's constant, q is the charge and r is the distance from the charge.

Additionally, the third charge may also experience a force due to the induced charges on the surface of the sphere. This force can be calculated using the formula for electric force, F = kqQ/r^2, where Q is the net charge on the sphere and r is the distance between the third charge and the centre of the sphere.

Overall, the introduction of a third charge near a neutral conducting sphere with cavities will cause a redistribution of charges and a change in the electric potential and field within the sphere. This is a complex system that can be analyzed using principles of electrostatics and is dependent on the properties of the third charge and the geometry of the cavities.