Electrostatics. Electric fields. Lecture 16 Electrostatics. Electric fields. Fundamentals of college physics (P.J. Nolan)

ELECTROSTATICS The study of electric charges at rest under the action of electric forces is called electrostatics Thales Miletus (624-547 B.C) Electric is derived from Greek word elektron, meaning amber The fundamental principle of electrostatics: like electric charges repel each other, whereas unlike electric charges attract each other

Atomic concept of electric charge 4. Fractional charged six quarks (Murray Gell-Mann, 1964) – up (u), down (d), strange (s), charm (c), bottom (b), top (t) 1. Atomic structure (Leucippus, Democritus, J.Dalton) 2. The electron (J.J. Thompson, 1897) a negatively charged particle having a mass 3. The proton (Rutherford, 1919), a positive charge 4. Neutron (J. Chadwick, 1932) The fundamental unit of charge, the coulomb, named after the French physicist Charles A. de Coulomb, is defined in terms of a certain number of electronic charges, That is, 1coulomb of charge is equal to

MEASUREMENT OF ELECTRIC CHARGE The electroscope

MEASUREMENT OF ELECTRIC CHARGE Conductors and insulators Materials that permit the free flow of electric charge through them are called conductors. Materials that do permit the free flow of electric charge through them are called insulators or dielectrics.

MEASUREMENT OF ELECTRIC CHARGE Charging by induction

MEASUREMENT OF ELECTRIC CHARGE The Faraday Ice Pail (1) A charge cannot exist by itself within a conductor, but rather is found on the outside of the conductor and (2) the electroscope leaves have the same net quantity of charge as that placed within the can

COULOMB`S LAW

COULOMB`S LAW The force between the point charges q1 and q2 is directly proportional to the product of their charges and inversely proportional to the square of the distance separating them. The direction of this force lies along the line separating the charges. This result is known Coulomb`s law for vacuum and air the permittivity of free space for air and vacuum

Comparison of the electric and gravitational forces between electron and proton

MULTIPLE CHARGES If there are three or more charges present, then the force on any one charge is found by the vector addition of the forces associated with other charges

Multiple charges all on same line

Multiple charges all on same line

Multiple charges not all on same line

Example. Charged pith balls. Two equally charged balls separated by 0 Example. Charged pith balls. Two equally charged balls separated by 0.100 m. find the charge on each ball and the tension in the string if the mass of each ball is , and the length l of the string is 0.250m.

THE LANGUAGE OF PHYSICS Electrostatics. The study of electric charges at rest under the action of electric forces The fundamental principle of electrostatics. Like electric charges repel each other, whereas unlike electric charges attract each other Quarks. Elementary particles of matter. There are six quarks. They are up, down, strange, charm, bottom, and top. The proton and neutron are made of quarks, but the electron is not. Conductors. Materials that permit the free flow of electric charge through them. Insulators or dielectrics. Materials that do not permit the free flow of electric charge through them Coulomb`s law. The force between point charges q1 and q2 is directly proportional to the product of their charges and inversely proportional to the square of the distance separating them. The direction of the force lies along the line separating the charges.

ELECTRIC FIELDS Coulomb`s law states only that there is a force and says nothing about the mechanism by which the force is transmitted Michael Faraday introduced the concept of an electric field. He stated that it is an intrinsic property of nature that an electric field exists in the space around an electric charge. This electric field is considered to be a force field that exerts a force on charges placed in the field. The electric field is measured in terms of a quantity called the electric field intensity. The magnitude of the electric field intensity is defined as ratio of the force F acting on the small test charge q0 to the small test charge itself. The direction of the electric field is in the direction of the force on the positive test charge. In SI

The electric field of a point charge The electric field intensity of a point charge is directly proportional to the charge that creates it, and inversely proportional to the square of the distance from the point charge to the position where the field is being evaluated.

Electric field of a positive point charge

Electric field of a negative point charge

Superposition of electric fields The force on a arbitrary charge q is the vector sum of the forces produced by each charge The superposition of electric fields states that when more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges

Superposition of electric fields

Superposition of electric fields

The electric field of charged conducting plate

The electric field of a parallel plate capacitor The field between the plates is uniform and parallel

Electric potential energy The potential energy of that charge can be defined as the energy it possesses by virtue of its position in the electric field. The potential energy is equal to the work that must be done to place that charge into that position in the electric field

The potential The electric potential V is defined as the potential energy per unit charge Note the analogy between the potential being a potential energy per unit charge and the electric field being a force per unit charge in SI If we know the potential and the distance between plates we can find the electric field intensity

The potential difference

Potential of a point charge If the two points A and B are not too far apart then as a first approximation we can use a geometric average Equation gives the potential at any point that is at a distance r from a point charge q

Potential of a point charge Plot of the potential function for a positive point charge

Potential of a point charge

Potential of a point charge The potential well of the negative point charge

Superposition of potentials The principle of superposition of potentials is stated: if there are a number of point charges present, the total potential at any arbitrary point is the sum of the potentials for each point charge. However, because the potentials are scalar quantities they add according to the rules of ordinary arithmetic. The potential at any point in the field of two like charges

Superposition of potentials The potential at any point in the field of two unlike charges (a dipole)

Dynamics of a Charged Particle in a Electric Field An electric charge is in an electric field If the charge is free to move, it will experience an acceleration

Example. Projectile motion of a charged particle in an electric field Example. Projectile motion of a charged particle in an electric field. A proton is fired at an initial velocity of 150m/s at an angle of above the horizontal into a uniform electric field of between two charged parallel plates. Find (a) the total time the particle is in motion, (b) its maximum range, and (c) its maximum height. Neglect any gravitational effects.