Unit 1 - Electrostatics Properties of Charge ● 2 types of charge: ○ Positive - absence of electrons ○ Negative - excess of electrons ● Unit of charge is Coulomb (C) ● Charge is quantized (exists in discrete values) ○ The smallest increment of charge is the charge of an electron ○ The charge on one electron is e = 1.6 x 10-19 C ○ q = n*e ■ q - total charge on an object ■ n - # of electrons ■ e - charge on an electron ● Charge is conserved ○ Charge is neither created nor destroyed ○ Simply move from one object to another Movement of charge ● Charge by contact ○ Charge is moved by touching two objects together ○ Charge is distributed among objects ○ The objects end up with the same type of charge In this example, Object A is negatively charged (a lot of electrons), and these electrons want to separate themselves as far as possible. When Object B touches A, some of the electrons transfer to B, causing Object B to be negatively charged and Object A to be the same type of charge, except with less charge than Object A had before. ● Polarization of charge ○ No change in the charge of either object ○ The charge rearranges while the objects are close together ○ Objects do not touch ● Charge by Induction ○ While the objects are being polarized, the neutral object is touched or grounded, allowing the polarized charges to escape ○ The objects end up with the opposite type of charge Coulomb’s Law ● Like charges repel ● Opposite charges attract ● If only two objects, the force on each is equal and opposite ● Force is a vector! ○ Find the direction from the relative polarities of the charges Electric Field ● The electric field is a force field similar to the gravitation field ● A charge placed in an electric field experiences a force of magnitude ● F is the force in N ● E is the electric field in N/C ● q is the charged place in the field of C ● A positive charge experiences a force in the same direction as the field. ● The electric field always points away from positive charges and towards negative charges Creating the Electric Field ● For a point charge ○ E is the electric field in N/C ○ k is Coulomb’s constant (9.0 x 109 N m2/C2) ○ q1 is the magnitude of the charge in C ○ r is the distance from the center in m ● For a conducting plate of uniform charge density ○ E is the electric field in N/C ○ σ is the charge density in C/m2 ○ ε0 is the electricity of permittivity of free space (8.85 x 10-12 C2 / (N m2) Electric Field due to a Continuous Charge Distribution ● For lines of charge, rings of charge and discs of charge ● Break the object into small bits of charge, dq. ● It’s important to include the direction in the calculations AP Daily 1.5 Video 2 AP Daily 1.5 Video 3 Electric Flux ● Electric flux measures the magnitude of the electric field through a given surface ● ● E is the electric field in N/C ● A is the area of the surface ● This is a dot product, so we need only the portion that is parallel to the area vector (which is perpendicular to the surface) AP Daily 1.4 Video 1 Electric Flux Through a Closed Surface ● If Flux goes from ○ Inside to outside (positive) ○ Outside to inside (negative) Gauss’ Law - VERY IMPORTANT! (Common question on AP) ● Gauss’ law is a tool for finding the electric field surrounding objects or systems that can be enclosed by a symmetrical surface AP Daily 1.4 Video 2 AP Daily 1.4 Video 3 AP Daily 1.4 Video 4 Electric Field: Sphere of Uniform Charge http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesph.html#c3 Electric Field due to a Thin Hollow Shell Electric Field due to an Infinite Plane Electric Field due to Parallel Plates Electric Field due to an Infinite Line Charge E = λ/(2πε0R) Electric Potential The Potential Energy of a Dipole The Electric Potential Inside a Parallel-Plate Capacitor The Electric Potential of a Point Charge The Electric Potential of Many Charges Unit 2 - Conductors, Capacitors, Dielectrics (Ch. 29) Connecting Potential and Field Batteries and EMF Finding the Electric Field from the Potential Kirchhoff’s Loop Law A Conductor in Electrostatic Equilibrium Capacitance and Capacitors Parallel Capacitors Charge: ADD Voltage: SAME Series Capacitors Charge: SAME Voltage: ADD The Energy Stored in a Capacitor Dielectrics The presence of the dielectric weakens the electric field Filling a capacitor with a dielectric increases the capacitance by a factor equal to the dielectric constant. Unit 3 - Electric Circuits The Electron Current Where Ne = the number of electrons Where the electron density ne = electrons per cubic meter The electron current is directly proportional to the electric field strength. Current Density Kirchhoff’s Junction Law Conductivity and Resistivity Resistance and Ohm’s Law More on Ohm’s Law Ohm’s law is limited to those materials whose resistance R remains constant—or very nearly so—during use. The materials to which Ohm’s law applies are called ohmic. Fundamentals of Circuits Energy and Power Real Batteries A potential difference V bat is called the terminal voltage. Series Resistor Parallel Resistor Voltmeters ● A device that measures the potential difference across a circuit element is called a voltmeter. ● Because potential difference is measured across a circuit element, from one side to the other, a voltmeter is placed in parallel with the circuit element whose potential difference is to be measured. Ammeter ● A device that measures the current in a circuit element is called an ammeter. ● Because charge flows through circuit elements, an ammeter must be placed in series with the circuit element whose current is to be measured. RC Circuits Charging a Capacitor Unit 4 - Magnetic Fields Magnetism Permeability Constant: Biot-Savart law RHR: thumb is the direction of velocity Magnetic Field of Current The magnetic field of a long, straight wire The magnetic field of a current loop A current loop is a magnetic dipole ≈ Where Magnetic Field of a Coil Center (z = 0) Ampère’s Law The magnetic field inside a current-carrying wire using Ampere’s Law Solenoids The Magnetic Force on a Moving Charge Cyclotron Motion The Hall Effect Hall Voltage: Forces and Torques on Current Loops Helical Paths Pitch = v|| * T, where v|| is the parallel component of the velocity and T is the period Radius r = mv⊥/(qB), where v⊥ is the component of the velocity perpendicular to the magnetic field. Unit 5 - Electromagnetism Motional emf Inducted Current: Force required to move the wire Power = Magnetic Flux Lenz’s Law Faraday’s Law where is an induced emf. Induced Fields Strength of the induced electric field inside the solenoid Induced Currents: Three Applications Generators ● ● Transformers ● ● 1 = Primary 2 = Secondary (V1 / V2) = (N1/N2) = (I2/I1) Metal Detectors ● Inductors inductance of the solenoid ● ● Energy LC Circuits 2πf = (1/(LC)1/2 LR Circuits (Equations are just like RC circuits)
