Is the Direction of Energy Flow in a Capacitor Correct?

[sachi]

In a parallel plate capacitor with circular plates we're asked to find the magnitude and direction of the poynting vector, which logically should be pointing radially outwards. Let us say that the top plate is positively charged and the bottom is negatively charged. Therefore we have an E-field and D field pointing downwards. Since Jd (the displacement current) is the time derivative of D, we should find the current pointing downwards. We can then work out the resultant B-field which acts in the direction indicated by the right hand rule (i.e into the page on the left side of the capacitor and out of the page on the right side of the capacitor). Now use N= E X H and the left hand rule to give us the direction of energy flow. The E-field points downwards. This indicates that energy is flowing into the capacitor which makes no sense. I'm not too sure where I've gone wrong.

 

[Meir Achuz]

You have assumed the capacitor is charging so that dD/dt is positive downward. Energy should flow into a charging capacitor.

 

[sachi]

surely energy flows from the circuit to which the capacitor is connected and not from the surroundings?
Also if we consider energy being dissipated in a wire we get a similar situation. let the current flow be into the page. this is also the direction of the electric field. by the right hand rule the B field is clockwise. Therefore using the left hand rule we see the poynting vector pointing inwards (in this case energy is definitely not going into the wire.)

 

[Meir Achuz]

The EM energy flow into the wire heats the wire up.