# Electric Field on Surface of Capacitor

If I have a dielectric (a piezoelectric, to be exact) sandwiched between two platinum plates (electrodes), and connect one end to positive potential of a battery and the other to ground (I don't even know why one has to connect the top to ground), and also connect the negative potential of a battery to ground, what is the electric field on the surface of the grounded plate? Where do the field lines coming from the bottom plate terminate?

I ask because I'm doing an experiment where I'm trying to put particles on top of an electrode on a piezoelectric plate to stretch them. The particle is field-sensitive (sensitive to electric fields) so I thought if I just ground the plate the particles are on, everything would be fine. However, just because the plate is at zero potential (grounded), does that mean the field on its surface is zero?

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The geometry is very unclear. Each plate has two surfaces, the "inside" touching the dielectric, and the "outside". Which surface are you asking about? In order to stretch the particles, they need to be connected to two things that are moving apart. Please tell us what BOTH of those two things are. Are they the two platinum plates? Or one platinum plate and something else? –  Steve B Jul 13 '12 at 13:53

## 1 Answer

There are opposing surface charges on the inner faces of both of the electrodes. The is also effective surface charges on the outer faces of the dielectric, due to its being polarized by the applied field. The field lines emanate from and terminate on these surface charges.


## The field up here is small

oooooooooooooooooooooooooo  -- outer surface of electrode, zero surface charge
++++++++++++++++++++++++++  -- inner surface, positive surface charge
--------------------------  -- surfaces of dielectric have surface charges
(bulk of dielectric)        -- due to induced polarization.
++++++++++++++++++++++++++  -- This polarization opposes the applied field
--------------------------  -- inner surface of other electrode, negative charge
oooooooooooooooooooooooooo  -- outer surface of electrode

## The field down here is small



The field outside of the capacitor should be small since the conducting plates ensure that no field escapes from the gap (it will be non-zero due to leakage from around the edges of the capacitor).

The fact that the field is small outside the capacitor is not directly related to the potential value associated with either plate.
It is related to the fact that the plates are (highly) conducting, the electrons in the metal can move around in response to any applied fields, and thus counteract them.

Most E&M textbooks should give some account of a parallel plate capacitor; the only reference I have handy is Chpt. 4 of Jackson.

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