Electric field outside two concentric sphere's

1. Jan 14, 2005

bulbanos

We've got two concentric metallic spheres, lets say P and Q
P is the smallest one, so its inside Q
Q is grounded and P is positive charged

I figured out that the field in between P and Q is not homogeneous but constant. But why is the field outside Q zero while it is not inside Q? Still the field is zero inside P because of the Gauss' Law...
I just don't see the profound difference between the two spheres.

2. Jan 14, 2005

vincentchan

You sure it is constant??? I don't think so... a paralleled metal plate will riase a constant E field in between, but not for a concentric sphere.. You may want to check your calcultion, the field should be similar to a point charge in free space

The field inside the Q is not zero is also because of gauss law.. draw an gaussian surface in between P and Q, the charge enclosed in the gaussian surface is surely not zero, $$Q_{enclosed}/ \epsilon = \int \vec{E} d \vec{S}$$.. so how could $$\vec{E}$$ be zero?

Q carries negative charge and P carries positive charge.. and there E field cancels out.. Question: Where did the negative charge come from?

Last edited: Jan 14, 2005
3. Jan 14, 2005

clive

If "constant" means "does not vary in time" (after equilibrium, obviously) then bulbanos is right. After equilibrium there is an electroSTATIC field.

The external sphere is grounded then V_Q=0. But this sphere is in the electrical field created by P (q/4/pi/eps_0/R_Q). R_Q is the radius of external sphere In order to have a zero potential, external sphere will get -q from Earth and will have its own potential -q/4/pi/eps_0/R_Q. The total potential of Q will be now given by the sum between the potential of the field from P and the potential from its own field that is 0.

In any external point, the field is zero because the electrical charge inside the Gaussian surface containing this point is 0: q+(-q)=0. (see the post of vincentchan for the Gauss' law)

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