Electricity & Magnetism: 22-26%

Front 1

Electric Forces, Fields, and Potential

Back 1

PART 1/4 (10%)

Front 2

Coulomb's Law
F= K x q1q2/r(2)
K(o)=1/(4(pi)E(o))

Back 2

-Electric force is analogous to gravitational force: the attraction or repulsion b/w two particles is directly proportional to the charge of the two particles and inversely proportional to the square of the distance b/w them.

-in the first equation, q1 and q2 are the charges of the two particles, r is teh distance b/w them, and k is a constant of proportionality. In a vacuum, this constant is Coulumb's constant, K(0), which is approximately 9x10(9).
-Coulomb's constant is often expressed in terms of a more fundamental constant-the PERMITTIVITY OF FREE SPACE, E(O), which has a value of 8.85x10(-12)

Front 3

Electric Potential Energy
ΔU = -W

Back 3

-B/c an electric field exerts a force on any charge in that field, and b/c that force causes charges to move a certain distance, we can say that an electric field does work on charges.
-Consequently, we can say that a charge in an electric field has a certain amount of POTENTIAL ENERGY, U.

Front 4

Work
W=qEd

Back 4

-the work done to move a charge is the force, F, exerted on the charge, multiplied by the displacement, d, of the charge in the direction of the force.
-As we saw earlier, the magnitude of the force exerted on a charge q in an electric field E is F(q)=qE. Thus, we can derive the equation for work on a charge.

Front 5

Work and Electric Fields Rules

Back 5

1.) When the charge moves a distance r parallel to the electric field lines, the work done is qEr.
2.) When the charge moves a distance r perpendicular to the electric field lines, no work is done.
3.) When the charge moves a distance r at an angle θ to the electric field lines, the work done is qEr cosθ.

Front 6

Potential Difference (Electric Potential) V
V = W/q

Back 6

-the voltage reading on a battery tells us the difference in potential energy b/w the positiv end and the negative end of the battery, which in turn tells us the amount of energy that can be generated by allowing electrons to flow from the negative end to teh positive end.
-is a measure of work per unit charge, and is measured in units of joules per coulomb, or VOLTS (V). One vole is equal to one joule per coulomb.

Front 7

Conductors

Back 7

-the electrons are only loosely bound to the nucleus and are quite free to flow.
-ex: copper, platinum, and most other metals

Front 8

Insulators

Back 8

-the electrons are quite tightly bound to the nucleus and cannot flow.
-ex: wood and rubber

Front 9

Circuits & Circuit Elements (DC Circuits) (p. 243-265)

Back 9

PART 2/4 (6%)

Front 10

Voltage (same as Potential Difference)
-Volt=Joule/Coulomb

Back 10

-to separate charges and create a positive and negative terminal, the battery must do a certain amount of work on the charges.
-this work per unit charge is called the voltage, V, or electromotive force, emf, and is measured in volts (V).
-the voltage of a battery is a measure of the work that has been done to set up a potential difference b/w the two terminals.

Front 11

Current
I = Q/t

Back 11

-is the charge per unit time across an imaginary plane in the wire.
-each electron moves toward the positive terminal at a speed V(d), called the DRIFT SPEED, which is only about one millimeter per second.
-the unit of current is the coulomb per second, which is called an AMPERE (A): 1A= 1C/s

Front 12

Resistance

R = ΔV/I

Back 12

-the current in the copper wire would be much larger than the current in the glass wire.
-glass wire has a higher RESISTANCE TO CURRENT.
-the unit of resistance is the OHM (Ω). One ohm is equal to one vol per ampere: 1Ω = 1 V/A.

Front 13

Ohm's Law
I = V/R

Back 13

-relates the three important quantities of current, voltage, and resistance.

Front 14

Resistivity
R = p L/A

Back 14

-or p, is a property of a material that affects its resistance. The higher the resistivity, the higher the resistance. Resistance also depends on the dimensions of the wire-on it's length, L, and cross-sectional area, A.

Front 15

Conductivity

Back 15

-syaing a material has high conductivity is another way of saying that material has a low resistivity.
-Similary, a circuit with high conductance has low resistance.
-Someone with half a sense of humor named the unit of conductance the ohm (Ω), where 1 Ω= 1Ω(-1).

Front 16

Heat

Back 16

-as current flows through a resistor, the resistor heats up. The heat in joules is given by:

H = I(2)Rt = Pt
-where t is the time in seconds. In other words, a resistor heats up more when there is a high current running through a strong resistor over a long stretch of time.

Front 17

Resistors in Parallel

Back 17

-two resistors are in parallel when the circuit splits in two and one resistor is placed on each of the two branches.
-it is often useful to calculate the equivalent resistance as if there were only one resistor, rather than deal with each resistor individually.
-Given two resistors, R1 and R2, in parallel, the equivalent resistance, R(t), is:
1/R(t)= 1/R1 + 1/R2

-the voltage drop must be the same across both resistors, so the current will be stronger for a weaker resistor, and vice versa.

Front 18

Determining Circuits in Parallel and in Series

Back 18

1.) Determine the equivalent resistance of the resistance of the resistors in parallel. 1/R1 + 1/R2

2.) Treating the equivalent resistance of the resistors in parallel as a single resistor, calculate the total resistance by adding resistors in series. (Add the parallel answer from 1 to the series).

Front 19

Voltmeters (v) and Ammeters (A)

Back 19

-a voltmeter (v), measures the voltage across a wire. It is connected parallel with the stretch of wire whose voltage is being measured, since an equal voltage crosses both branches of two wires connected in parallel.
-an Ammeter (A), is connected in series. It measures the current passing through that point on the circuit.

Front 20

Fuse

Back 20

-a fuse burns out if the current in a circuit is too large.
-this prevents the equipment connected to the circuit from being damaged by the excess current.
-For example, if the ammeter in the previous problem were replaced by a half-ampere fuse, the fuse would blow and the circuit would be interrupted.

Front 21

Kirchhoff's Rules

Back 21

1.) The Junction Rule helps us to calculate the current through resistors in parallel and other points where a circuit breaks into several branches.
2.) The Loop Rule helps us to calculate the voltage at any point in a circuit.

Front 22

The Junction Rule (Kirchoff's Rules)

Back 22

-tells us how to deal with "junctions", where a circuit splits into more than one branch, or when several branches reunite to form a single wire.
-THE CURRENT COMING INTO A JUNCTION EQUALS THE CURRENT COMING OUT.
-This rules tells us how to deal with resistors in series and other cases of circuits branching in two or more directions. If we encounter three resistors in series, we know that the sume of the current through all three resistors is equal to the current in the wire before it divides into three parallel branches.

Front 23

Loop Rule (Kirchoff's Rules)

Back 23

-addresses the voltage drop of any closed loop in the circuit.
-THE SUM OF THE VOLTAGE DROPS AROUND A CLOSED LOOP IS ZERO.

Front 24

Voltage Rules

Back 24

-Voltage drops by IR when the loop crosses a resistor in the direction of the current arrows.
-Voltage rises by IR when the loop crosses a resistor against the direction of the current arrows.
-Voltage rises by V when the loop crosses a battery from the negative terminal to the positive terminal.
-Voltage drops by V when the loop crosses a battery from the positive terminal to the negative terminal.

Front 25

Capacitators

Capacitance: C = Q/ΔV

C = E(o) x A/d

Back 25

-a device for storing charge, made up of two parallel plates with a space b/w them.
-The plates have an equal and opposite charge on them, creating a potential difference b/w the plates.
-can be made of conductors of any shape, but the PARALLEL-PLATE CAPACITOR is the most common kind.
-in a circuit diagram, a capacitor is represented by two equal parallel lines.
-the unit of capacitance is the Farad (F). One farad is equal to one coulomb per volt. Most capacitors have very small capacitances, which are usually given in microfarads, where 1 µF = 10(-6) F.

Front 26

Energy

Back 26

-to move a small amount of negative charge from the positive pate to teh negative plate of a capacitor, an external agent must do work. This work is the origin of the energy stored by the capacitor.

Front 27

Equivalent Capacitance

Back 27

-Like resistors, capacitors can be arranged in series or in parallel. The rule for adding capacitance is the reverse of adding resistance:
-CAPACITORS IN SERIES ADD LIKE RESISTORS IN PARALLEL, AND CAPACITORS IN PARALLEL ADD LIKE RESISTORS IN SERIES.

-2 Capacitors in series:
1/C(t) = 1/C(1) + 1/C(2)

-2 capacitors in parallel:
C(t) = C(1) + C(2)

Front 28

Dielectrics
E(new) = E(old) - E(induced) =
E/k

Back 28

-one way to keep the plates of a capacitor apart is to insert an insulator called a dielectric b/w them.
-a dielectric increases the capacitance.
-there is an electric field b/w the plates of a capacitor. This field polarizes the molecules in the dielectric; that is, some of the electrons in the molecules move to the end of the molecules, near the positive plate.
-The movement of electrons creates a layer of negative charge by the positive plate and a layer of positive charge by the negative plate. This separation of charge, in turn, creates an electric field in the dielectric that is in the opposite direction of the original field of the capacitor.
-This reduces the total electric field: formula given.
-the greek letter k is called the dielectric constant, and it varies from material to material. For all material, k>1.
-If the potential difference across the capacitor is too large, then the electric field will be so strong that the electrons escape from their atoms and move towards the positive plate. T

Front 29

Magnetic Fields and Forces (p.271-281)

Back 29

PART 3/4 (6%)

Front 30

Permanent Magnets

Back 30

-permanent magnets are made up of atoms that have electrons orbiting a nucleus of protons and neutrons.
-these electrons create miniscule magnetic fields. These tiny fields all point in different random directions, so the bulk material does not have a magnetic field. But in permanent magnets, the fields are all lined up together, and to the material is MAGNETIZED.
-Materials, like iron, that can be magnetized, are called FERROMAGNETIC.
-Other materials, like wood or plastic, which have atoms that won't line up in this fashion and can't create magnetic fields, are called PARAMAGNETIC.
-In the same way that semiconductors straddle the fence b/w conductors and insulators, there are DIAMAGNETIC materials that are not quite ferromagnetic or paramagnetic. Diamagnetic materials produce weak magnetic fields.

Front 31

Calculating Magnetic Force

Back 31

-a magnetic field exerts a force on a moving charge. Given a magnetic field, B, and a charge, q, moving with velocity, v, the force, F, on the charge is:
F = q (v x B)
-Magnetic field strength is measured in TESTLAS (T), where 1T = 1 N/A x m.

Front 32

Direction of the vxB vector using the RIGHT-HAND RULE:

Back 32

-point the fingers of your right hand in the direction of the velocity vector and then curl them around to point in the direction of the magnetic field vector. The direction in which your thumb points gives you the direction of the vxB vector.
F = qvBsinθ

Front 33

Trajectory Of Charges in a Magnetic Field

Back 33

-The magnitude of the velocity will not change, but charged particles moving in a magnetic field experience nonlinear trajectories.

Front 34

Magnetic Fields and Electric Fields Overlapping

Back 34

-There's not reason why a magnetic field and an electric field can't operate in the same place.
-Both will exert a force on a moving charge. Figuring out the total force exerted on the charge is pretty straightforward: you simply add the force exerted by the magnetic field to the force exerted by the electric field.

Front 35

Magnetic Force on Current-Carrying Wires

Back 35

-When dealing with a current in a wire, we use Il, where I is the current in a wire, and l is the length, in meters, of the wire-both qv and Il are expressed in units of C.m/s.
-equation for the magnitude of a magnetic force in order to apply it to a current-carrying wire:
F = IlBsinθ

Front 36

Magnetic Field Due to a Current

B = U(o) I / 2πr

Back 36

-magnetic field has an effect on a moving charge, and A MOVING CHARGE, OR CURRENT, CAN GENERATE A MAGNETIC FIELD.
-the constant u(o) is called the PERMEABILITY OF FREE SPACE, and in a vacuum it has a value of about 4πx10(7) N/A(2).

Front 37

Electromagnetic Induction (p. 289-297)

Back 37

PART 4/4 (1%)

Front 38

Magnetic Flux Φ

Back 38

-the magnetic flux, Φ, through an area, A, is the product of the area and the magnetic field perpendicular to it:
Φ = B.A = BAcosθ
-the A vector is perpendicular to teh area, with a magnitude equal to the area in question. If we imagine flux graphically, it is a measure of the number and length of flux lines passing through a certain area.

Front 39

3 Ways of Changing Magnetic Flux (ΔΦ)

Back 39

1.) Change the magnetic field strength.
2.) Change the area.
3.) Rotate the area, changing the angle b/w the area and the magnetic field.

Front 40

Faraday's Law
lEl = ΔΦ/Δt

Back 40

-induced emf is a measure of the change in magnetic flux over time.

Front 41

Lenz's Law

E = - (ΔΦ/Δt)

Back 41

-the current flows so that it opposes the change in magnetic flux by creating its own magnetic field.
-tells us in what direction that current flows.
-using the right-hand rule, we point out humb in the opposite direction of the change in magnetic flux, and the direction in which our fingers wrap into a fist indicates the direction in which current flows.

Front 42

The Electric Generator "Dynamo"

Back 42

-is a noisy favorite at outdoor events that need electricity.
-it uses the principle of electromagnetic induction to convert mechanical energy-usually in the form of a gas-powered motor-into electrical energy.
-A coil in the generator rotates in a magnetic field. As the magnetic flux through the coil changes, it induces an emf, creating a current.

Front 43

The Transformer

Back 43

-the transformer converts current of one voltage to current of another voltage. A simple transformer consists of two coils wrapped around an iron core.
-transformers rely on the property of MUTUAL INDUCTION: the change in current in one coil induces an emf in another coil. The coil with the applied current is called the primary coil, and the coil with the induced emf is called the secondary coil.
-The induced emf is related to the emf in the primary coil by the number of turns in each coil:

emf in secondary/emf in primary =
number of turns in secondary/number of turns in primary

Front 44

Magnetic Field & Electric Field
•F(E) = -F(B)
•qE = -q(v x B)
•E = -(v x B)

Back 44

-Initially, the magnetic field ismuch stronger than the electric field, but as more electrons are drawn to the bottom of the bar, the electric field becomes increasingly stronger.