Transcript Spherical and Cylindrical Capacitors

Spherical and Cylindrical
Capacitors
Gautam Chebrolu
Ryan Dickmann
Spherical

How it looks:

An inner sphere(solid) of a radius of R1
and a radius of R2 to the outer shell.
Spherical(Calculations)

First find the Electric Field outside the
sphere:
◦ Make a spherical Gaussian surface around it
◦ The change in Electric Potential, or Voltage, is equal to
the integral of the Electric Field from inner to outer
radius
Spherical(Calculations)

Since charge on each plate is equal to the product of
Capacitance and Electric Potential, reordering the
equation gives:

Plugging in the found Voltage the charge symbols cancel
and give:
Cylindrical

How it looks:
An inner cylinder(solid) of a radius of R1
and a radius of R2 to the outer shell.
 It is similar to the spherical capacitor.

Cylindrical(Calculations

First find the Electric Field around the
cylinder using Gauss’ Law:
 Where lambda is the linear charge density

The Voltage is equal to the integral of the
Electric Field from inner to outer radius
Cylindrical(Calculations)

Since charge on each plate is equal to the product of
Capacitance and Electric Potential, reordering the
equation gives:

Plugging in the found Voltage the charge
symbols cancel and give:
Which is Capacitance per Unit Length