ELECTRIC FIELDS, POTENTIAL DIFFERENCE & CAPACITANCE

The fundamental rule at the base of all electrical phenomena is that like charges repel and opposite charges attract.

ELECTRIC FIELD A charge creates an electric field around it in all directions. When another charged object enters this electric field, it experiences an electric force (magnitude and direction).

Michael Faraday developed the concept of an electric field. ELECTRIC FIELD

MR. CHARGE BABY CHARGE

Here is a positive charge (+Q). What is the strength of the electric field (E) at a point that is distance d from the charge? d E = ?

Electric field strength (E) is defined as the force experienced by a small positive test charge (+q) when it is placed at a point some distance (d) from the charge. d +

Here is a negative charge (-Q). What is the strength of the electric field (E) at a point that is distance d from the charge? d E = ?

Electric field strength (E) is defined as the force experienced by a small positive charge +q when it is placed at that point. d +

ELECTRIC FIELD INTENSITY

Overview Problems Problem 1 Problem 2 Problem 3

ELECTRIC FIELDS The direction of the electric field at any point is the direction that a positive charge (+q) would move when placed at that point.

ELECTRIC FIELDS Electric Field Lines are imaginary lines drawn so that their direction at any point is the same as the direction of the electric field at that point.

The strength of the electric field is indicated by the spacing between the lines. The closer the electric field lines the stronger the electric field. ELECTRIC FIELDS

POSITIVE CHARGE The electric field lines around a positive charge will point away from the charge.

NEGATIVE CHARGE The electric field lines around a negative charge will point towards the charge.

TWO POSITIVE CHARGES

POSITIVE & NEGATIVE CHARGE

B A B A WHICH CHARGE IS STRONGER A OR B?

A good conductor contains charges that are not bound to any atom and are free to move within the material. When no net motion of charges occurs within a conductor, the conductor is said to be in electrostatic equilibrium. ELECTROSTATIC EQUILIBRIUM

2. Any excess charge on an isolated conductor resides entirely on its surface. 1. The electric field is zero everywhere inside the conductor. PROPERTIES OF AN ISOLATED CONDUCTOR

4. On an irregularly shaped conductor, the charge tends to accumulate at sharp points. 3. The electric field outside a charged conductor is perpendicular to the conductor’s surface. PROPERTIES OF AN ISOLATED CONDUCTOR

ROBERT VAN DE GRAAFF

VAN DE GRAAFF At Museum of Science

Consider a fixed negative charge placed at a point B and a fixed positive charge at point A. There is a force of attraction between the two charges. Point A Point B ENERGY AND ELECTRICAL POTENTIAL

Work has to be done against the force of attraction to move the negative charge from point B to point C. Therefore negative charge will have a change in its potential energy. Point A Point B Point C ENERGY AND ELECRICAL POTENTIAL Point B

 measured in volts  the change in potential energy (work) per unit charge. ELECTRICAL POTENTIAL DIFFERENCE

Use this formula when the work on a charge is given.

Derived Equation:

Use this formula when working with parallel plates (uniform electric field)

Overview Problems Example Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9

Parallel Plates When two parallel plates are connected across a battery, the plates will become charged and an electric field is established between them.

PARALLEL PLATES Since the field lines are parallel and the electric field is uniform between two parallel plates, a test charge would experience the same force of attraction or repulsion no matter where it was located. F = q x E

The direction of the electric field is defined as the direction that a positive test charge would move if placed in the field. So in this case, the electric field would point from the positive plate to the negative plate. The field lines are parallel to each other and so the electric field is uniform.

V measured in Volts (V) E measured in Newtons/Coulomb (N/C) d measured in meters (m) Therefore 1 N/C = 1 V/m

Since the field lines are parallel and the electric field is uniform between two parallel plates, a test charge would experience the same force of attraction or repulsion no matter where it was located. That force is calculated with the equation: F = q E

In the diagram above, the distance between the plates is 0.14 meters and the voltage across the plates is 28V. If a positive 2 nC charge were inserted anywhere between the plates, it would experience a force in the direction of the negative, bottom plate, no MATTER where it is placed in the region between the plates.

WHAT HAPPENS TO E AS d INCREASES & DECREASES E and d have an inverse relationship (mathematically)

Millikan Oil Drop Experiment Robert Millikan discovered the charge of an electron.

Millikan Oil Drop Experiment Fine oil drops were sprayed from an atomizer in the air. Gravity acting on the drops caused them to fall. A potential difference was placed across the plates. The resulting electric field between the plates exerted a force on the charged drops. The resulting electric field between the plates was adjusted to suspend a charged drop between the plates.

REMEMBER  An electron always carries the same charge.  Charges are quantized.  Changes in charge are caused by one or more electrons being added or removed.

Capacitor A device designed to store electric charge. A typical design of a capacitor consists of two parallel metal plates separated by a distance. The plates are connected to a battery. Electrons leave one plate giving it a positive charge, transferred through the battery and to the other plate giving it a negative charge. This charge transfer stops when the voltage across the plates equals the voltage of the battery. Thus the charged capacitor acts as a storehouse of charge and energy that can be reclaimed when needed for a specific application.

The capacitance (C) of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference (voltage) between the conductors. C = Capacitance (Farad) (F) Q = Charge (Coulomb) (C) V = Potential Difference (Volts) (V)

Overview Problems Example Problem 10 Problem 11