Electric Charge, Forces, and Fields Electric charge is a property of many elementary particles. There is a basic unit of charge that apparently cannot be subdivided: The Coulomb is the SI unit of charge. There are two types of charge called positive and negative. The electron carries a charge of –e, while the proton carries +e. Charges exert forces on each other. Opposite charges attract, charges of the same sign repel.

Coulomb’s Law The force that two point charges exert on each other is governed by Coulomb’s Law: This is an inverse square law, so if R triples, F decreases by 1/9, etc.

Exercise: A 4 µC charge is located at (0, 3) and a -2 µC is located at (2, 0). Find the force exerted on a -3 µC charge at the origin. One can calculate the force due to several charges by first calculating the force due to each individual charge, then using vector addition on the individual forces. This is an illustration of the principle of superposition.

Imagine a “distribution of charge”, for example, several discrete charges spread over some region of space. Now imagine a small + charge placed anywhere in the region. Will the “test charge’ experience a force? Yes, the total coulomb force created by all the other charges. The test charge experiences the electric field, E, created by the other charges:

The electric field exists even if there is not a charge present to experience it. In a sense, we are attributing properties to points in space where matter may not be present. Of course these properties are not arbitrary and depend on the matter (and in this case its charge) that is “nearby”. Note that the direction of E is set by what would happen to a + charge. What will be the effects on a – charge? Force will be in opposite direction, but field direction is not determined by the charge that is “experiencing” it. Example: Field due to a single charge R Q q

Field Lines One can depict the electric field in a region with a device known as “field lines”. These satisfy two criteria: 1) Electric field is tangent to the field lines 2) Strength of electric field is directly proportional to density of lines Field lines emanate out of + charges and end on – charges.

Field lines start on + charges, end on – charges. The electric field is tangent to field lines

When several charges are present, one can employ the principle of superposition to determine the net field at a point. Each charge contribution is unaffected by the presence of the other charges. Exercise: Find the field at the origin due to a +3µC at (4, 0) and a -5µC at (0, -2) E+E+ E-E-

Motion in an electric field When a charged particle enters an electric field, it experiences a force: Newton’s 2nd law then says; If the field is uniform, then the force and acceleration are constant, and we can use our simple motion equations to describe the motion. Example: Find the acceleration an electron experiences in a uniform field of 1000 N/C.

Exercise: An electron enters a region of uniform electric field 4000 N/C directed down. The electron is moving horizontally at 2x10 4 m/s. How much is it deflected after traveling 1 cm? Horizontally: Vertically: