Question

14. (14 points) A solid elliptical conductor with a net charge +Q is surrounded by a hollow spherical conductor with net charge -Q. Points a & c are on the outer surface of the inner conductor, and points b and d are on the inner surface of the outer conductor as shown. Compare yab, the magnitude of the potential difference between points a and b, to Vcd, the magnitude of the potential difference between points c and d. A) VAB VcD B) Vab = VcD C) Vab < VcD How do the electric field intensities between the two pairs of locations compare? A) EAB ECD B) EA8 = Eco C) EAB < EcD D) The field between the conductors is zero

Will give an up vote only if all parts are answered and detailed explanations are given. Thank you.

Answer 1

Each conductor is an equipotential.

Potential at points a and c is equal (V_{​​​​​a}=V_{​​​​​c}).

Potential at points b and d are equal (V_{​​​​​​b}​​=V_{​​​​​​d}).

$V_{ab}=V_{a}-V_b$

$V_{ab}=V_{c}-V_d$

$\boxed {V_{ab}=V_{cd}}$

Electric field is the gradiant of electric potential. The magnitude of electric field is more if the rate of change of electric potential with position is more. From the previous results, the change in potential between points a & b and points c & d are equal. But the separation between points c and d is larger than the separation between points a and b. So, the electric potential changes faster between points a and b. Therefore, the electric field is higher between points a and b than between points c and d.

$\boxed {E_{ab}> E_{cd}}$