Electric Charge, Forces, and Fields

Electric Charge

We already know:

Electric charge is a fundamental property of matter

There are two electric charges: positive or negative (arbitrarily named)

The atom consists of a small positive nucleus surrounded by a negative electron cloud

Electric Charge

Like charges repel; unlike charges attract.

As with Mass/Energy: Charge is conserved

The net charge of an isolated system remains constant.

This is another fundamental law in physics

Electric Charge

SI unit of charge: the coulomb, C. All charges in nature are integer multiples of the charge on the electron:

Conductors

Most atoms hold on to their electrons tightly and are insulators. In aluminum, the valence electrons are essentially free and strongly repel each other. Any external influence which moves one of them will cause a repulsion of other electrons which propagates, "domino fashion" through the conductor.

In a conducting material, the outer electrons of the atoms are loosely bound and free to move through the material.

Conductors

Property of material: conductivity

1.Conductors transmit charges readily.

2.Semiconductors are intermediate; their conductivity can depend on impurities and can be manipulated by external voltages.

3.Insulators do not transmit charge at all.

Electrostatic ChargingObjects can have excess charge of one polarity or another. An electroscope may be used to determine if an object is electrically charged.

Electrostatic Charging

An electroscope can be given a net charge by conduction – when it is touched with a charged object, the excess charges flow freely onto the electroscope.

Electric Force

The force exerted by one charged particle on another is given by:

Electric Force

If there are multiple charges, the force vectors must be added to get the net force on another charge.

We can say that charges produce an “electric field” (and similarly, masses produce a “gravitational field”). The field describes the force felt by a test charge if it were placed into the field

Electric Field

Definition of the electric field: force on a charge if there were a charge

The direction of the field is the direction the force would be on a positive charge.

Electric FieldCharges create electric fields, and these fields in turn exert electric forces on other charges.

Electric field of a point charge:(Pointing away from the charge)

Electric FieldFor multiple charges, the total electric field is found using the superposition principle:For a configuration of charges, the total, or net, electric field at any point is the vector sum of the electric fields due to the individual charges.

Electric FieldExample: electric field from three point chargesThree point charges are located on a circular arc as shown in the figure below. (Take r = 3 cm. Let to the right be the +x direction and up along the screen be the +y direction.)

Answer: from symmetry, E has no y-component, the x component is given by:

= same field as if a single charge with +1 nC was located at the point where the negative charge is

Rules for drawing electric field lines:

1. Closer lines mean a stronger field.

2. The field is along the lines at every point.

3. Field lines start on positive charges and end on negative charges.

4. The number of lines entering or leaving a charge is proportional to the magnitude of the charge.

5. Field lines never cross.

It’s convenient to represent the electric field using electric field lines. These lines are drawn so the field is along the line at every point.

Electric Field

Electric Field: examples

Electric field lines of a dipole:

A dipole is an arrangement of charge with positive charge on one end and negative charge on the other.

From far away, the dipole is “invisible”, i.e. it looks neutral.

Close to the dipole, the electric field looks as drawn on the left.

Electric Field: examples

Electric field lines of a dipole:

Threads in oil with two charged spheres: threads have electric dipole and so line up with field, can “see” electric fierd lines

Electric Field: examples

Electric field lines due to very large parallel plates:

Superposition: fields not normal to surface cancel

Electric Field: examples

Electric field lines due to like charges:

(a)equal charges

(b)unequal charges

Electric FieldOften, tricks and symmetry considerations can help us find electric fields in a problem. Consider equal 8 charges arranged equally spaced around a circle:

What’s E-field at P, center of the circle?

What if we take one charge away?

Taking one charge away is the same as adding a negative charge to that position. Superposition principle says the E-field is the same as the field coming from one negative charge

Conductors and Electric Fields

Electric charges are free to move within a conductor; therefore, there cannot be a static field within the conductor:

1) The electric field is zero inside a conductor

Excess charges on a conductor will repel each other, and will wind up being as far apart as possible.

2) Any excess charge on a conductor resides entirely on the surface of the conductor

There cannot be any component of the electric field parallel to the surface of a conductor; otherwise charges would move.

3) The electric field at the surface of a charged conductor is perpendicular to the surface

Conductors and Electric Fields

Conductors and Electric Fields

The force from neighboring charges is less when the curvature of the surface is large:

Excess charge tends to accumulate at sharp points, or locations of highest curvature, on charged

conductors. As a result, the electric field is greatest at such locations.

Conductors and Electric Fields

Electric field is strongest near sharp points: That is why lightning rods have sharp points, and why lightning strikes buildings with sharp points.

Lightning happens when an electric field in the Earths atmosphere becomes so large that electrons are ripped off of atoms in the air