a)A dielectric in the shape of a thick-walled cylinder of outer radius R1 = 5.15 cm, inner radius R2 = 3.65 cm, thickness d = 3.95 mm, and dielectric constant κ = 3.87 is placed between the plates, coaxial with the plates, as shown in the figure. Calculate the capacitance of capacitor B, with this dielectric.
It is unclear whether the plates are the curved inner and outer surfaces of the hollow cylinder, or planar surfaces perpendicular to the axis of the cylinder.
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To calculate the capacitance of capacitor B with the given dielectric, you can use the formula:
C = κ * ε₀ * A / d
where:
C is the capacitance
κ is the dielectric constant
ε₀ is the vacuum permittivity (8.854 x 10^-12 F/m)
A is the area of the capacitor plates
d is the distance between the plates
To find the area of the capacitor plates, you need to calculate the difference between the outer and inner areas of the thick-walled cylinder.
The area of the outer surface (A1) can be calculated using the formula for the area of a circle:
A1 = π * (R1^2)
Similarly, the area of the inner surface (A2) can be calculated as:
A2 = π * (R2^2)
Now, you can calculate the difference in area (A) as:
A = A1 - A2
Next, convert the given thickness (d) from millimeters to meters:
d = 3.95 mm = 0.00395 m
Finally, plug the values into the capacitance formula:
C = κ * ε₀ * A / d
Substitute the known values:
C = 3.87 * (8.854 x 10^-12 F/m) * A / 0.00395 m
Simplify the equation and calculate the value of C.