# J(dot)E = Work/Volume

1. Aug 14, 2011

### AriAstronomer

Hey guys,
So I know I'm missing something really stupid, but I can't figure out what it is.
I'm seeing the claim that the current density dotted with the Electric field is equal to Work per volume, or: J.E = W/V. Using dimensional analysis though, I keep getting an extra unit of seconds on the left hand side of the denominator:
(Cm/m^3s)(N/C) = J/(m^3)
Nm/sm^3 = J/m^3
J/sm^3 = J/m^3

What am I doing wrong?
Thanks,
Ari

2. Aug 14, 2011

### cepheid

Staff Emeritus
I get the same answer as you using the fact that the electric field has dimensions of voltage / length. Then J*E becomes

[C/(sm2)] * V/m

= (C*J/C)*m-3s-1

= Jm-3s-1

Where exactly are you "seeing this claim?"

3. Aug 15, 2011

### takudo_1912

W isn't "work" ,it's work/t(its dimension is J/s),you mistakes at this

4. Aug 15, 2011

### matonski

Yeah J dot E is power per unit volume. That's usually the starting point for deriving expressions for the poynting vector and the energy density in the field.

5. Aug 15, 2011

### AriAstronomer

Ahh Power/Volume. Thanks. I had seen this claim on a flashcard, I'm preparing for GRE's and got a bunch of flash cards sent from a school to help me. Must be a typo on their part then.

Ari