Answer:
Explanation:
a)
Using Ohms Law
[tex]R= \rho \frac{l}{\pi a^2 } \\V = IR = E l = I \rho \frac{l}{\pi a^2 } \\E = \frac{I \rho}{\pi a^2 } \\E = J \rho [/tex]
Where J is the current density [tex]J = \frac{I}{\pi a^2 } [/tex]
and the direction of E is the same as the direction of the current. Since J is uniform throughout the conductor [tex]E = \rhoJ[/tex] just inside at a radius a (and anywhere else).
b)
Since we have no changing electric fields we can use Ampere’s law in it’s simplest form without displacement current
[tex]\oint B .dl = B 2 \pi a = \mu_{o} I [/tex]
such that
[tex]B = \frac{\mu_{o} I}{2 \pi a } [/tex]
and by the right hand rule, since the current is going to the right, the magnetic field is circling around the conductor such that it’s pointing out of the page at the top and into the page at the bottom.
c)
The Poynting vector is given by
[tex]S = \frac{1}{ \mu_o} |E \textrm{x}B| = \frac{\rho I^2}{2 \pi^2 a^3} [/tex]
and by the right hand rule it’s always pointing in towards the center of the conductor.
d)
Note: directions of these three vectors are mentioned along with their magnitudes in above 3 parts a , b and c
