EE140 Mid-Term 1 Dr. Ray Kwok Print Name : _______________________________________________________________________ 1. A long coaxial cable of radius “a” is carrying a non-uniform current density zrJˆ2 (into the page). The outer shield is a grounded conductor and a dielectric r is filled between b and c. B = 0 in the grounded shield b < r < c. (a) What are the magnetic fields inside the cable? (b) Use the formula sJHHn )(ˆ212 to derive the surface current density at r = a and r = b. a b cEE140 Mid-Term 1 Dr. Ray Kwok Q Q d x y O 2. Consider 2 point-charges, +Q at y = d and –Q at the origin as shown. a. What is the electric field vector at a point on the x-axis (x,0,0) ? b. With dEV, find the electric potential at a distance d away on the x-axis (d,0,0). c. Compare this result with the potential using the point charge equation.EE140 Mid-Term 1 Dr. Ray Kwok 3. (a) What is the electric potential of a uniformly charged ring of radius R at a distance z away from the center (as shown)? (b) Using the result from part (a), derive the electric potential of a charged disc with non-uniform surface charge density s = a r2, at a distance z away from the center as shown? (c) From this electric potential, write the electric field vector of the charged disc at this location z using .VE z z R
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