Lecture 4 Van de Graff Generator Millikan’s Oil-Drop Experiment Electric Flux and Gauss’s Law Potential Difference Capacitance

Experiments to Verify Properties of Charges Faraday’s Ice-Pail Experiment Concluded a charged object suspended inside a metal container causes a rearrangement of charge on the container in such a manner that the sign of the charge on the inside surface of the container is opposite the sign of the charge on the suspended object Millikan Oil-Drop Experiment Measured the elementary charge, e Found every charge had an integral multiple of e Oil drop exp.Oil drop exp. q = n e

Fig , p.515

Fig b, p.515

Electric Flux Field lines penetrating an area A perpendicular to the field The product of EA is the flux, Φ

Fig , p.517

Electric Flux, cont. Φ E = E A cos θ The perpendicular to the area A is at an angle θ to the field When the area is constructed such that a closed surface is formed, use the convention that flux lines passing into the interior of the volume are negative and those passing out of the interior of the volume are positive

Gauss’ Law Gauss’ Law states that the electric flux through any closed surface is equal to the net charge Q inside the surface divided by ε o ε o is the permittivity of free space and equals 8.85 x C 2 /Nm 2 The area in Φ is an imaginary surface, a Gaussian surface, it does not have to coincide with the surface of a physical object

Electric Field of a Charged Thin Spherical Shell The calculation of the field outside the shell is identical to that of a point charge The electric field inside the shell is zero

Fig , p.522

Electric Field of a Nonconducting Plane Sheet of Charge Use a cylindrical Gaussian surface The flux through the ends is EA, there is no field through the curved part of the surface The total charge is Q = σA Note, the field is uniform Gaussian surface Gaussian surface

Electric Field of a Nonconducting Plane Sheet of Charge, cont. The field must be perpendicular to the sheet The field is directed either toward or away from the sheet

Parallel Plate Capacitor The device consists of plates of positive and negative charge The total electric field between the plates is given by The field outside the plates is zero

Electric Potential Energy The electrostatic force is a conservative force It is possible to define an electrical potential energy function with this force Work done by a conservative force is equal to the negative of the change in potential energy

Work and Potential Energy There is a uniform field between the two plates As the charge moves from A to B, work is done on it W = Fd=q E x (x f – x i ) ΔPE = - W = - q E x (x f – x i ) only for a uniform field

Fig. 16-2, p.533

Potential Difference The potential difference between points A and B is defined as the change in the potential energy (final value minus initial value) of a charge q moved from A to B divided by the size of the charge ΔV = V B – V A = ΔPE / q Potential difference is not the same as potential energy

Potential Difference, cont. Another way to relate the energy and the potential difference: ΔPE = q ΔV Both electric potential energy and potential difference are scalar quantities Units of potential difference V = J/C A special case occurs when there is a uniform electric field V = V B – V A = -E x x Gives more information about units: N/C = V/m

Energy and Charge Movements A positive charge gains electrical potential energy when it is moved in a direction opposite the electric field If a charge is released in the electric field, it experiences a force and accelerates, gaining kinetic energy As it gains kinetic energy, it loses an equal amount of electrical potential energy A negative charge loses electrical potential energy when it moves in the direction opposite the electric field Demo

Energy and Charge Movements, cont When the electric field is directed downward, point B is at a lower potential than point A A positive test charge that moves from A to B loses electric potential energy It will gain the same amount of kinetic energy as it loses in potential energy

Summary of Positive Charge Movements and Energy When a positive charge is placed in an electric field It moves in the direction of the field It moves from a point of higher potential to a point of lower potential Its electrical potential energy decreases Its kinetic energy increases

Summary of Negative Charge Movements and Energy When a negative charge is placed in an electric field It moves opposite to the direction of the field It moves from a point of lower potential to a point of higher potential Its electrical potential energy increases Its kinetic energy increases Work has to be done on the charge for it to move from point A to point B

Electric Potential of a Point Charge The point of zero electric potential is taken to be at an infinite distance from the charge The potential created by a point charge q at any distance r from the charge is A potential exists at some point in space whether or not there is a test charge at that point