b) A dielectric in the shape of a thick-walled cylinder of outer radius R 1 = 4.

Question

b) A dielectric in the shape of a thick-walled cylinder of outer radius R1 = 4.39 cm, inner radius R2 = 2.89 cm, thickness d = 1.75 mm, and dielectric constant ? = 1.91 is placed between the plates, coaxial with the plates, as shown in the figure. Calculate the capacitance of capacitor B, with this dielectric.

c) The dielectric cylinder is removed, and instead a solid disc of radius R1 made of the same dielectric is placed between the plates to form capacitor C, as shown in the figure. What is the new capacitance?

Explanation / Answer

a)

C = k _o A/d = 1 * 8.85e-12 * 3.1416*4.39e-2*4.39e-2/1.75e-3 = 3.06e-11 F

B)

C = C1 + C2

= k1e0A1/d + k2e0A2/d

= (1*8.85e-12*3.1416*0.0289*0.0289/1.75e-3) + (1.91*8.85e-12*3.1416*(0.0439*0.0439-0.0289*0.0289)/1.75e-3)

= 3.06 * 10^-11 F

C)

C1 = k1e0A1/(d/2) = 1*8.85e-12*3.1416*0.0439*0.0439/(1.75e-3/2) = 6.12e-11 F

C2 = k2e0A2/(d/2) = 1.91*8.85e-12*3.1416*0.0289*0.0289/(1.75e-3/2) = 4.0256e-11

C = C1C2/(C1+C2) = ( 1.9079e-11*4.0256e-11)/( 1.9079e-11+4.0256e-11)

==> C = 2.77 * 10^-11 F

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