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Unformatted text preview: 4, 5. Following a procedure similar to the one illustrated in examples 4.7 and 4.8, determine the
capacitance of two concentric spherical conductors of radii a and b when a spherical dielectric
shell of thickness djs placed concentrically between the conductors as shown in Figure P4.5a.
The dielectric shell has an inner radius c and dielectric constant e = e, 5,. Show that the total
capacitance is the sum of three series capacitances each with a homogeneous dielectric layer as shown in Figure P4.5b. Figure P4.5 Geometry of spherical capacitor ﬁlled with multilayer dielectric. 4.5. (a) D is continuous, therefore ID - ds = Q DJ r2 sin 9d9d¢ = 4m2Dr = Q D Q r=4m_2 r<b '9
% c+d C
c+d c a
_ _LU .12.de 4.31m [—13er
47:80 .5 r c+d£rr gr
c+d c a
= Q l +_1_ +1
47:80 rb err” 1"c
7 47:50 c+d b s c c+d a c
a5 1 -1 LG- 1 )+.L_},
c+d b er c c+d a c
Using —1—=—1—7i+i,then C (II 6'2 C3 i-1(1_l) i- 1 [1-1] i_1[i_l)
ci 47:30 c+d b’ c 43180.9r c c+d’ c3 47:50 a c ...
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This note was uploaded on 08/13/2010 for the course EE EE 335 taught by Professor Xaio during the Spring '10 term at Cal Poly.
- Spring '10