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20092ee1_1_EE_1_HW_5

20092ee1_1_EE_1_HW_5 - perfect dielectric for which ε r =...

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EE1; Homework 5: DUE MAY 14TH THURSDAY 5 PM (THERE IS A COLLECTION BOX NEAR MARIKO WALTON’S CUBICLE IN 66-127 ENGR IV ) 1) A parallel-plate capacitor is made using two circular plates of radius a , with the bottom plate on the xy plane, centered at the origin. The top plate is located at z = d , with its center on the z axis. Potential V 0 is on the top plate; the bottom plate is grounded. Dielectric having radially-dependent permittivity fills the region between plates. The permittivity is given by 0 ( ) (1 ) a ρ ε ρ ε = + . Find: a) V(z) b) E G c) Q d) C 2) Two conducting spherical shells have radii a = 3 cm and b = 6 cm. The interior is a
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Unformatted text preview: perfect dielectric for which ε r = 8. (a) Find C. (b) A portion of the dielectric is now removed so that ε r = 1.0, 0 < φ < π /2, and ε r = 8, π /2 < φ < 2 π . Again, find C. 3) (a) Find the electric field ( E ) on the z-axis for z = h > 0 ? (b) Find the electric field ( E ) on the z-axis for z = -k where k<d? (c) Find the electric field ( E ) on the z-axis for z = -k where k>d? 4) Find the capacitance of an isolated conducting sphere of radius b that is uniformly coated with a dielectric layer of thickness d. The dielectric constant is given by ε ....
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