Calculating Poynting Vector in Resistive Rod

[bon]

Homework Statement

Consider a long resistive rod exhibiting resistance R of length l and radius r. Calculate the magnitude and direction of the poynting vector (neglecting edge effects) and relate the rate of energy transfoer between the rod and its exterior to the total power dissipated in the rod.

Homework Equations

N = 1/mu 0 ExB

The Attempt at a Solution

Just not sure how to do this?

Do i assume a current I flows in the rod and find E(r) inside the rod and B(r) inside the rod? I am confused...

thanks

 

[anathema]

for any help!
Thank you for your question. To calculate the magnitude and direction of the Poynting vector, you will need to use the formula N = 1/mu 0 ExB, as you mentioned. However, in order to apply this formula, you will need to first calculate the electric field and magnetic field inside the rod.

To do this, you can assume a current I is flowing through the rod, as you suggested. Then, you can use the formula for the electric field inside a cylindrical conductor to calculate E(r) inside the rod. Similarly, you can use the formula for the magnetic field inside a long straight conductor to calculate B(r) inside the rod.

Once you have calculated E(r) and B(r), you can plug them into the formula for the Poynting vector to find its magnitude and direction. Remember to also consider the direction of the current flow when determining the direction of the Poynting vector.

As for the relationship between the rate of energy transfer and the total power dissipated in the rod, you can use the formula P = IV to calculate the power dissipated in the rod, where I is the current flowing through the rod and V is the voltage across the rod. Then, you can compare this value to the rate of energy transfer, which is given by the magnitude of the Poynting vector.

I hope this helps you with your problem. Good luck with your calculations!