• Electric field

The cathode ray tube is perhaps best known today as the old television or old computer monitor. It is a relatively simple device that had its beginnings as a fundamental scientific research tool. The experiments conducted on these early cathode ray tubes led to the development of better vacuum tubes, electronic components such as valves and eventually to television picture tubes.

In the experiments carried out by J.J. Thomson, he subjected cathode rays to known electric and magnetic fields, measured the resulting deflections, and from these measurements was able to work out the charge-to-mass ratio for the particles that made up the rays.

Before we can understand what he did, we will have to learn a bit more about the forces exerted on charged particles by both sorts of field. We will start with the electric field.

We imagine that a charge is surrounded by an electric field and that this field exerts a force on any other charge placed in the field.

The strength of the electric field at a point is defined as the force that a +1 coulomb charge would experience if placed at the point.

• Representing or mapping an electric field

A number of rules apply to the interpretation of these lines of force diagrams.

• Field lines begin on positive charges and end on negative charges.
• Field lines never cross.
• Field lines that are close together represent strong fields.
• Field lines that are well separated represent weak fields.
• A positive charge placed in the field will experience a force in the direction of the arrow.
• A negative charge placed in the field will experience a force in the direction opposite to the arrow.
• Uniform electric field

A uniform electric field can be made by charging two parallel plates which are separated by a small distance compared with their length. These electric fields are very useful in physics and were used by prominent scientists such as Robert Millikan and J.J. Thomson when investigating the properties of small charged particles.

• Force acting upon a charged particle in an electric field

The direction of the force that a positive and negative charge would experience if placed in an electric field.

As seen above the electric field is determined by finding the force acting on a unit charge placed at that point.

The symbol for electric field is $$\vec{E}$$, the symbol for electric field magnitude is E.

$$\vec{E} = \dfrac{\vec{F}}{q}$$

$$\therefore E = \dfrac{F}{q}$$

where

E = electric find intensity (in newtons per coulomb)

F = electric force (in newtons, N)

q = electric charge(in coulombs, C)

Therefore the force acting upon a particle carrying a charge q and placed in an electric field of $$\vec{E}$$  is given by the formula:

$$\vec{F} = q \vec{E}$$

$$\therefore F = qE$$

Between two charged plate the electric field is uniform and the magnitude of the electric field, E, is given by:

$$E = \dfrac{V}{d}$$

Hence the magnitude of the force acting upon a particle carrying a charge q placed between two charged parrallel plates is given by the formula

$$F = q \dfrac{V}{d}$$

This can be derived by recalling that potential difference is the change in potential energy per unit charge moving from one point to the other. The amount of energy or work is given by:

$$W = qV$$

Remember that work done is equal to the gain in energy.

• Energy transformation during the motion of a charged particle between two charged parallel plates

A small positive charge released next to the positive plate from point A will experience a force that will accelerate the charge toward the negative plate.

The charge will increase its kinetic energy, work is done by the electric field. We can calculate the speed of the particle at any point B between the plates.