Magnitude of electric field between two concentric oppositely charged

[sa1988]

Homework Statement

Magnitude of electric field between two concentric oppositely charged spheres.

Homework Equations

The Attempt at a Solution

So I first went with the simple electric field equation E=V/d

So I have the potential difference V between the two sphere surfaces. I can't do Latex but hyperphysics has it anyway:

So I know V.
And surely, in E=V/d, the distance d is simply b-a.

So finally I sub my V and d into the equation and I'm left with:

E = Q/(4πεab)

Which looks reasonable enough.. But all sources on the Internet tell me that the answer is simply:

E=Q/4πεr²

The real confusing thing for me here is... What is 'r' ? What is it the radius from? The radius from the centre? Or from the surface of the inner sphere? Or something else..??

I fear my problem may be with the fact that I used E=V/d, which is possibly only valid for charged plates, rather than spheres? Either way, I'm still a little confused about what the 'r' actually means in the correct answer.

Thanks for any guidance :thumbs:

 

[sa1988]

Should 'r' be defined such that:

a < r < b

?

 

[BvU]

The expression above the $\Delta V$ formula you show is that selfsame E=Q/(4πεr²) !
Read up on Gauss's theorem (ibidem, another two lines higher up, or Gauss's law)

Your E=V/d is a special case for a constant $\vec E$ all over the place.
Otherwise (here for instance) $\vec E = -\vec\nabla V$.

And r is simply the distance to the center.

 

[sa1988]

Oh dear oh dear! So yeah I guess my main error was for the E=Vd part.

I've been taught about E = -∇V before, and yeah that makes perfect sense come to think of it.

Electric/Magnetic fields is certainly my weakest subject at the moment. Must study harder!

Thanks for showing me that :thumbs: