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Unformatted text preview: PRELIM 1 ECE 303 28 September 2004 NAME 50/Â»:7â€˜1 â€˜W, SECTION 1. (30 points) Consider a capacitor consisting of two thin conducting spherical shells of
radii a and b (with b > a). The space between the shells is ï¬lled with two different
dielectrics, as shown, with each occupying half the space. If the inner conductor is
charged to +V volts and the outer conductor is grounded (at zero volts), what is the total
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grounded (at zero potential) plane at 2:0, and that there is a charge +Q at the point (x21,
y=0, z=l) and a charge +2Q at the point (x23, y=0, z=3). Derive (a) an expression for
the electric potential V(x, y, z) everywhere in space, and (b) find the surface charge
density on the plane. Assume the medium above the conductor is free space. â€˜ v:7 ,
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p3 : (X_,)1+L)2+lj3/L +[CY}y.+71+7]3/2_ [ohm +1 4U [(X 3)+ j PRELIM 1 ECE 303 28 September 2004 NAME SECTION 3. (30 points) Shown at left is a sphere, centered at the
origin, with a radius a, a permittivity 8 that is different
from so, and with a constant charge density pv
everywhere in the shaded region, i.e., everywhere except
in the spherical hole, which has a radius of a/4 and is
centered at x=a/4. Find the electric ï¬eld everywhere on
the xaxis (only). The hole and the region outside the
sphere have the permittivity of free space. ï¬‚â€. 0< )5 qr (Pfâ€”yâ€”cptgf, â€œan X '> O 3 r3 I, r . 31" ,Dâ€˜m oâ€˜Vâ€˜Pcf)
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 Fall '06
 RANA
 Electromagnet, Electric charge, free space, Dielectrics, conducting spherical shells, charge density pv, +V volts

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