Coulomb’s Law Performing electric field calculations on charge distributions in an X-Y coordinate Plane

Coulomb’s Law: Calculates the electrostatic force that exists between charged point charges. Where F ES = Electrostatic Force (N) k = Coulomb’s Constant (9.0 * 10 9 Nm 2 /c 2 ) Q1 & Q2 = charge of point charges (coulombs) r = distance between point charges (m) The force can be attractive or repulsive.

Electric Fields Regions in space that distort the normal behaviors of charged particles such that they will experience a given amount of force per unit charge present at the field point. The field exists because of the presence of given source points containing a net charge.

Electric Field Vector An electric field is a vector quantity but the field itself is actually an infinite number of vector quantities spread out over a plane. An electric field is defined as force per unit charge. E 0 = electric field vector (N/c) F 0 = electrostatic force on q 0 (N) q 0 = charge (C) at field point

Points in an Electric Field Source Point(s) – Point charges at a given location in a charge distribution that are contributing to the electric field at the field point. Field Point – The point at which the electric field vector is calculated in a charge distribution. If there is a charge contained at the field point it is typically not considered in calculating the field at that location.

The Superposition Principle The electric field caused by individual point charges can each be evaluated at a given field point and the result can be combined with that from other point charges using vector addition.

The Superposition Principle This can be applied to any number of source points. It can also be applied to deal with continuous charge distributions (continuous lines or rings of charge) by breaking them up into a large number of point charges spaced close together. This means a wide variety of fields can be modeled on a spreadsheet.

Energy and Potential in Electric Fields Electric potential energy comes from work done by electrostatic forces. –It is calculated for a specific charge in a field. Electric potential is energy per UNIT charge and usually refers to a position in an electric field compared to a reference position (usually infinitely far away) –It is calculated for a specific location in a field

For a single charge there is no PE For a single point charge the potential can be calculated at various locations around the charge but there is no potential energy present until there is another charge present. When there is a 2 charge system the potential can be calculated at any location surrounding the charges but the PE can only be calculated for either one of the charges.

Electric Potential Energy (2 Point charges) Like Charges very close together will tend to accelerate apart due to a large electrostatic repulsion Like charges far apart will tend to accelerate apart due to electrostatic repulsion but are already far separated so do not reach the same velocity.

Electric Potential Energy Opposite charges very close together will tend to accelerate together due to a large electrostatic attraction but over a small distance so little work is done. Opposite charges very far apart will tend to accelerate together due to electrostatic attraction but over a large distance so a lot of work is done.

Field Equations for a Single Point Charge Electric Field (vector) Electric Potential (scalar)

Objectives: Calculate the field (and force on the field point) produced by any number of point charges as well as the field created by a continuous charge distribution Calculate the potential of a location (or potential energy of a point charge) given a number of point charges

Tips/Troubleshooting The IF functions are present in order to prevent errors caused by dividing by zero. Electrostatic force and potential energy are calculated when a charge is located on the field point. This is not necessary for the field and potential. Look at the graph to be able to view the charge distribution to better understand the results.

AP 3D Supplement How to model a continuous a ring of charge.

Use 628 point charges Polar coordinates can be used to make a circle: Y coordinate = Rsin  X coordinate = Rcos  –R is the radius of the ring specified on the spreadsheet and  is counted from 0 to 6.28 (0 to 2  radians) in increments of The charge is 1/628 th of the total charge possessed by the ring.

The Superposition Principle Allows for using Coulomb’s Law multiple point charges to form an electric fields The spreadsheet can calculate the field created by the 628 charges individual charges which closely approximates a continuous ring of charge. Follow the instructions on the document and good luck.