Week 4: Capacitance 155
Problem 4.
Find the capacitance of the following arrangements:
b a
c
A A
d d
where the first two are parallel plate capacitorshalf-filledwith a dielectric material with relative
dielectric permittivityǫras shown, and the third is a spherical capacitor patially-filled with thesame
dielectric as shown.
Problem 5.
Derive the rules for adding parallel and series capacitance:
1
Ctot=
1
C 1
+
1
C 2
+
1
C 3
+... (series)and
Ctot=C 1 +C 2 +C 3 +... (parallel)
Problem 6.
A conducting sphere of radiusahas a chargeQon it. It is surrounded by a spherical insulating
dielectric shell of inner radiusa, outer radiusband relative dielectric permittivityǫr. Find the field
in all space, the potential in all space, and the bound surface charge on both surfaces of the dielectric
in terms of the givens.