# Displacement and electric field

1. Jan 7, 2014

### chemphys1

1. The problem statement, all variables and given/known data

displacement and electric field related by D=εE where dielectric constant depends on volume and temperature. Express dD in terms of dV, dT and dE

(this is just a part of a question but want to make sure I have it right else the rest of the 'showing' and proofs are never going to work out)

3. The attempt at a solution

so taking D=εE

Then dD = εdV (because it is volume dependent) + εdT (temperature dependent)

what happens to the E, is it Edε + edE aswell as the above
although it can't be dε because it says express in terms of dT dV and dE, no dε mentioned?

is any of that on the right lines?

any help appreciated

2. Jan 7, 2014

### haruspex

We can write that predicate statement as ε = ε(V, T).
Based on that, you need to find an expression for dε in terms of dV and dT.
What would be the change in ε if T stays constant and V increases by dV?

3. Jan 7, 2014

4. Jan 7, 2014

### chemphys1

as in like this?

dε = (∂ε/∂V)dV + (∂ε/∂T)dT

where does dD =
come into this?

5. Jan 7, 2014

6. Jan 7, 2014

### chemphys1

come up with this

dD = E∂ε + εdE

where

dε = (∂ε/∂V)dV + (∂ε/∂T)dT

overall

dD = E [(∂ε/∂V)dV + (∂ε/∂T)dT] + εdE

is that what I should be getting?

7. Jan 7, 2014

Excellent!