Constant potential inside spherical shell

[physicsjock]

Hey,

I just wanted to double check if what I am thinking is correct.

Say you have a spherical shell of inner radius R1, and outer radius R2, which is made of a perfect conductor carrying a charge q1.

E=0 inside (r<R1) (and also between R1<r<R2 but not worried about that)

So the potential inside the shell is constant.

Now, say there is another charge centered inside the shell,

Is it correct to think that the charge remains in its position as the potential inside the shell is constant?

So if you were to bump the charge slightly (very slightly so its barely moving) it would simply move in the direction it was pushed at a constant velocity? And this is because the potential is constant within the shell so there is no other force acting on the charge?


Thanks in advance,

 

[gneill]

Hey,

I just wanted to double check if what I am thinking is correct.

Say you have a spherical shell of inner radius R1, and outer radius R2, which is made of a perfect conductor carrying a charge q1.

E=0 inside (r<R1) (and also between R1<r<R2 but not worried about that)

So the potential inside the shell is constant.

Now, say there is another charge centered inside the shell,

Is it correct to think that the charge remains in its position as the potential inside the shell is constant?

So if you were to bump the charge slightly (very slightly so its barely moving) it would simply move in the direction it was pushed at a constant velocity? And this is because the potential is constant within the shell so there is no other force acting on the charge?

Well, there's no net electric force acting on the charge; but there's no evidence about any other forces that may or may not be acting (gravitational, inertial).

 

[physicsjock]

Yea fair enough, I didn't mention any other forces.

I was just trying to understand constant potential a little better.

Disregarding any other outside forces, is it correct to say since the potential is constant (no force acting), if the charge inside the spherical shell were pushed it would simply move in the direction it was pushed at a constant velocity (assuming it was only pushed a very small amount)?

 

[gneill]

Yea fair enough, I didn't mention any other forces.

I was just trying to understand constant potential a little better.

Disregarding any other outside forces, is it correct to say since the potential is constant (no force acting), if the charge inside the spherical shell were pushed it would simply move in the direction it was pushed at a constant velocity (assuming it was only pushed a very small amount)?

Yes, it is true for "mundane" scenarios (non relativistic velocities).

I'll just point out that a constant potential means a zero electric field, since the field is the gradient of the potential. No field means no force.

 

[asteriatic]

Scientist

Hello Scientist, yes, your understanding is correct. Inside a spherical shell with a constant potential, the electric field is zero, which means there is no force acting on any charge inside the shell. Therefore, if you were to bump a charge inside the shell, it would continue to move at a constant velocity in the direction it was pushed, as there are no other forces acting on it. This is a result of Gauss's law, which states that the electric field inside a conductor is zero. Keep up the good thinking!