Electric Field Inside and Outside of a Cylinder

cylinder_app

The demonstration is designed for big auditoriums and should prove to students that an electric charge is collected on the outer surface of a cylinder, and that there is no electric field inside the cylinder.

Materials:

  • 4 light balls with conductive coating
  • Insulating thread
  • Conducting hollow cylinder (not grounded) with a connected conducting rod to mount conductive balls
  • Banana cable with electrical tape
  • Van de Graaff Generator

Demonstration:

Thread two of the conducting balls to the external component of the rod such that the balls rest against the outer sides of the cylinder. Thread the other two balls to the internal component of the rod such that they hang inside of the cylinder. Tape one side of a banana cable to the Van de Graaff generator with electrical tape and connect the other side to the inner rod in the cylinder apparatus.

To build up static charge on the cylinder, turn on the Van de Graaff generator, set it to a moderate speed, and leave it running. Static charges will build up on the outside of the cylinder, indicated by the outer conductive balls suspended in air, while the inside will remain electrically neutral, where the balls remain unchanged.

Turn off the Van de Graff generator and discharge it using its grounded discharging sphere before handling to prevent electric shock.

Explanation:

Some definitions:

  • Q = Total charge on Cylinder
  • r = Radius of cylinder
  • h = Cylinder length
  • A = Surface area of cylinder = 2πrh
  • E = Electric field force due to a point charge = \cfrac{Q}{4\pi\epsilon r}
  • ε = permittivity of free space(constant)

Before the Van de Graaf generator is turned on, the entire system is electrically neutral. After turning the generator on, static charges build up primarily on the outer surface of the cylinder. Electrons can move freely in a conductor and will move to the outside of the cylinder to maximize the distance between each electron. There is slightly more surface area on the outside of the surface than on the inside, so the electrons travel to the outside to have more space between one another, as like charges repel.

This is shown by the outer balls suspended in air in opposition to the static charges on the outside of the cylinder. They initially gain static charges while the cylinder is building up charge from contact with the cylinder, and when the static electric force becomes greater than the gravitational force keeping the ball downward, the ball electric field pushes the light ball away from the charged cylinder:

mgy < \cfrac{Q}{4\pi\epsilon r}

Where the left hand side indicates the gravitational force on each ball, and the right hand side indicated the force on the ball due to the electric field produced by like charges.

The inner balls remain unaffected by the electric field because there is no build up of static charge on the inside of the cylinder, so no charges are transferred via contact. The electrons are inclined to move to the outside of the cylinder, where the surface area is larger.

Notes:
1. Instructor should be cautious with the Van de Graff generator.
2. When setting up the demonstration, position the cylinder in front of and far from the Van de Graaff generator to prevent generator’s strong electric field from interfering with the balls. Use a long banana cable.
3. The discharge sphere can shock you if used improperly. A safer alternative is to use a wooden rod with a banana lead at its tip, attached to the ground of the Van de Graaff. The demo room will provide this for you.
4. Do not use the Van de Graaf with the black base (pictured here). Use instead the slightly smaller one with the blue base (safer).

 

Written by Lydia Seymour.