Question

A cylindrical wire has radius a and length L. A voltage V is applied along its length. Current will flow with uniform \( \vec{j} \) through the wire. Assume \( \vec{E} \) is also uniform in the wire, and that the wire is long and straight and lies on the z-axis in such a way that the current flows in the +z direction. a) Determine an expression for \( \vec{E} \) inside the wire. Your expression may only contain V, L, a, and a unit vector, but not necessarily all of those. (Yeah, this one's easy.) b) Determine an expression for \( \vec{B} \) inside the wire. (Yes, you've done this before.) c) Determine an expression for the magnitude and direction of the Poynting vector inside the wire. d) Using your answer to part c, determine the energy that flows away from this wire per second. Compare this to the power dissipated in a wire due to heating.

          A cylindrical wire has radius a and length L. A voltage V is applied along its length. Current will flow with uniform \( \vec{j} \) through the wire. Assume \( \vec{E} \) is also uniform in the wire, and that the wire is long and straight and lies on the z-axis in such a way that the current flows in the +z direction.
a) Determine an expression for \( \vec{E} \) inside the wire. Your expression may only contain V, L, a, and a unit vector, but not necessarily all of those. (Yeah, this one's easy.)
b) Determine an expression for \( \vec{B} \) inside the wire. (Yes, you've done this before.)
c) Determine an expression for the magnitude and direction of the Poynting vector inside the wire.
d) Using your answer to part c, determine the energy that flows away from this wire per second. Compare this to the power dissipated in a wire due to heating.

A cylindrical wire has radius a and length L. A voltage V is applied along its length. Current will flow with uniform j⃗ through the wire. Assume E⃗ is also uniform in the wire, and that the wire is long and straight and lies on the z-axis in such a way that the current flows in the +z direction.
a) Determine an expression for E⃗ inside the wire. Your expression may only contain V, L, a, and a unit vector, but not necessarily all of those. (Yeah, this one's easy.)
b) Determine an expression for B⃗ inside the wire. (Yes, you've done this before.)
c) Determine an expression for the magnitude and direction of the Poynting vector inside the wire.
d) Using your answer to part c, determine the energy that flows away from this wire per second. Compare this to the power dissipated in a wire due to heating.

Added by Alfredo W.

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