AP Physics III.A Electrostatics

18.1 Origin of Electricity

The Fundamental Charge (Robert Millikan and his oil drop experiment)

Ex. How many electrons are in two Coulombs of negative charge?

18.2 Charged Objects and Electric Force

Law of Conservation of Charge – during any one process, net electrical charge of an isolated system remains constant.

Ex. Two identical isolated conducting spheres, one with charge -6 μC and another with net charge +2 μC are allowed to touch. If the two spheres have the same net charge after touching, what is the net charge on each sphere?

Attractions and repulsions

18.3 Conductors and Insulators

18.4 Charging by Induction and Conduction (also known as, “I wish I had a decent electroscope”)

Charging by Conduction

Charging by Induction

Induced charge on an insulator

18.5 (Charles De) Coulomb’s Law

“Hmm, this looks like something I’ve seen before”

Ex. An electron “orbits” the proton of a hydrogen atom at an average distance of 0.53 EE m. What is the force that the proton exerts on the electron? What is the velocity of the electron for a circular orbit?

Ex. Two charges exert electrical force F on each other. If the magnitude of each charge is doubled and the distance between them is halved, what is the force F′ on each charge in terms of F?

Electric forces and vectors

Ex. Three Charges in a Line

Ex. Three Charges in a Plane

III.A.2 Electric Fields and Electric Potential

A mass in a gravitational field

Charges experience an electrostatic force due to the presence of other charges

An electric field is a vector that has a direction that the force exerts on a positive test charge.

Some examples

Ex. Find the electric force on a proton placed in an electric field of 2.0 EE 4 N/C that is directed along the positive x-axis.

Electric fields are vectors. The net electric field at a point in space can be determined by considering the contributions of each charged object and adding them together as vectors.

Ex. Electric Field Between Two Point Charges. Two point charges are separated by a distance of m. One has a charge of –25.0 μC and the other 50.0 μC. a) What is the magnitude and direction of the electric field at point P between them m from the negative charge? b) If an electron is placed at rest at P, what is the magnitude and direction of its initial acceleration?

Symmetry and the electric field.

Electric Field Lines

Notes about field lines Electric field lines originate on positive charges and terminate on negative charges The density of the field lines per unit area shows the strength of the field (uniform and non-uniform fields) Electric field lines are perpendicular to the surface of a charged object The direction of the field is tangent to any point on the field line Electric field lines do not cross (Why not?)

Field lines around positive and negative charges

Field lines between plates of a capacitor.

Field lines between two dipoles

Field lines between two identical charges

Electric Potential Energy

Work done on a charge in a uniform electric field

Muy importante – the displacement of the charge is in the direction of the electric field.

Let’s clarify but not overemphasize the signs

Electric Potential Difference

Let’s look at “gravitational potential” first

So change in electric potential is...

Electric potential decreases or increases not because the field exerts any more or less force (the field is uniform – like gravity near the Earth’s surface). V changes because of distance. A charge released in the field, traveling a greater distance converts more of its U e to K (like dropping an object from a greater height).

Everyday examples

Potential (and therefore potential difference) is scalar (this will simplify some things).

Summary Electric potential energy – energy a charge has because of its potential in an electric field (so far the field is uniform) Electric potential – electric potential energy per unit charge Potential difference – change in electric potential

Another formula “Ed has potential” V = −Ed (only true for a uniform electric field)

Ex. In the figure shown, the work done on a 2.0 µ C charge by the electric field from A to B is 5.0 EE -5 J. What is the change in electric potential energy and the potential difference? A ·A · B ·B ·

Worth noting: a positive charge accelerates from a higher potential to lower potential. A negative charge accelerates from lower potential to higher potentials.

Conservation of Energy – yep, here it is again with electrical potential energy in the picture

Ex. A proton is released in a uniform electric field with a magnitude of 8.0 EE 4 V/m directed along the positive x-axis. The proton undergoes a displacement of 0.50 m in the direction of the field. a) Find the change in electrical potential energy. b) Find the potential difference. c) Find the speed if the proton starts from rest.

Ex. A particle with mass of 1.8 EE -5 kg and a charge of 3.0 EE - 5 C is released from rest at point A and accelerates horizontally to point B. The only force on the particle is the force from the electric field and the electric potential at A is 25 V greater than the potential at B. What is the velocity of the particle at B?

Electric Potential Due to a Point Charge (requires calculus, sorry no proof today. Take AP Physics C and I will prove it for you next year.)

Important to use the signs when finding the potential of a point charge. Graphically – potential from a positive charge is positive and decreases to zero at infinity.

Potential from a negative charge is negative and increases towards zero at infinity.

Electric Potential for a Pair of Point Charges

Ex. A 5.0 µC charge is at the origin and a -2.0 µC charge is on the x-axis at (3.0, 0) m. a) If the electric potential is zero at infinity, find the total electric potential due to the charges at P, with coordinates (0, 4.0) m. b) How much work is required to bring a third charge of 4.0 µC from infinity to P?

Ex. How many places are there on the line below where the potential is zero? Where is (are) these locations? 2q2q-q-q

Ex. Potential energy for a group of charges

Equipotential Lines (or surfaces)