Few examples on calculating the electric flux Find electric flux

Gauss’s Law

Applications of the Gauss’s Law Remember – electric field lines must start and must end on charges! If no charge is enclosed within Gaussian surface – flux is zero! Electric flux is proportional to the algebraic number of lines leaving the surface, outgoing lines have positive sign, incoming - negative

Examples of certain field configurations Remember, Gauss’s law is equivalent to Coulomb’s law However, you can employ it for certain symmetries to solve the reverse problem – find charge configuration from known E-field distribution. Field within the conductor – zero (free charges screen the external field) Any excess charge resides on the surface

Field of a charged conducting sphere

Field of a thin, uniformly charged conducting wire Field outside the wire can only point radially outward, and, therefore, may only depend on the distance from the wire l- linear density of charge

Field of the uniformly charged sphere Uniform charge within a sphere of radius r Q - total charge - volume density of charge Field of the infinitely large conducting plate s- uniform surface charge density

Charges on Conductors Field within conductor E=0

Experimental Testing of the Gauss’s Law

Stable equilibrium with other constraints Earnshaw’s theorem A point charge cannot be in stable equilibrium in electrostatic field of other charges (except right on top of another charge – e.g. in the middle of a distributed charge) Stable equilibrium with other constraints Atom – system of charges with only Coulombic forces in play. According to Earhshaw’s theorem, charges in atom must move However, planetary model of atom doesn’t work Only quantum mechanics explains the existence of an atom

Electric Potential Energy Concepts of work, potential energy and conservation of energy For a conservative force, work can always be expressed in terms of potential energy difference Energy Theorem For conservative forces in play, total energy of the system is conserved

Potential energy U increases as the test charge q0 moves in the direction opposite to the electric force : it decreases as it moves in the same direction as the force acting on the charge

Electric Potential Energy of Two Point Charges

Electric potential energy of two point charges

Example: Conservation of energy with electric forces A positron moves away from an a – particle a-particle positron What is the speed at the distance ? What is the speed at infinity? Suppose, we have an electron instead of positron. What kind of motion we would expect? Conservation of energy principle

Electric Potential Energy of the System of Charges Potential energy of a test charge q0 in the presence of other charges Potential energy of the system of charges (energy required to assembly them together) Potential energy difference can be equivalently described as a work done by external force required to move charges into the certain geometry (closer or farther apart). External force now is opposite to the electrostatic force

Electric Potential Energy of System The potential energy of a system of two point charges If more than two charges are present, sum the energies of every pair of two charges that are present to get the total potential energy

Reading assignment: 23.3 – 23.5