# ElectroMag Overview

## READ THIS SHORT ARTICLE BY LAWRENCE KRAUSS FIRST

*** THEN WRITE 150 WORDS IN YOUR NOTEBOOK (TITLE IT: LK ARTICLE) SUMMARIZING THE THREE PAGES *** ## What is on the AP Physics C  (E & M)  Test?

A .  Electrostatics  30%

1 .  Charge and Coulomb’s law

2 .  Electric field and electric potential (including point charges)

3 .  Gauss’s law

4 .  Fields and potentials of other charge distributions

B .  Conductors, capacitors, dielectrics 14%

1 .  Electrostatics with conductors

2 .  Capacitors

a .  Capacitance

b .  Parallel plate

c .  Spherical and cylindrical

3 .  Dielectrics

C .  Electric circuits 20%

1 .  Current, resistance, power

2 .  Steady-state direct current circuits with batteries and resistors only

3 .  Capacitors in circuits

b .  Transients in RC circuits

D .  Magnetic Fields 20%

1 .  Forces on moving charges in magnetic fields

2 .  Forces on current-carrying wires in magnetic fields

3 .  Fields of long current-carrying wires

4 .  Biot–Savart law and Ampere’s law

E .  Electromagnetism 16%

1 .  Electromagnetic induction (including Faraday’s law and Lenz’s law)

2 .  Inductance (including lR and lC circuits)

3 .  Maxwell’s equations

## SAME LIST, MUCH MORE DETAIL (print this out and use it as a checklist):

A. Electrostatics   (30%)

1. Charge and Coulomb’s Law

a) Students should understand the concept of electric charge, so they can:

❒  (1) Describe the types of charge and the attraction and repulsion of charges.

❒  (2) Describe polarization and induced charges.

b) Students should understand Coulomb’s Law and the principle of superposition, so they can:

❒  (1) Calculate the magnitude and direction of the force on a positive or negative charge due to other specified point charges.

❒  (2) Analyze the motion of a particle of specified charge and mass under the influence of an electrostatic force.

2. Electric field and electric potential (including point charges)

a) Students should understand the concept of electric field, so they can:

❒  (1) Define it in terms of the force on a test charge.

❒  (2) Describe and calculate the electric field of a single point charge.

❒  (3) Calculate the magnitude and direction of the electric field produced by two or more point charges.

❒  (4) Calculate the magnitude and direction of the force on a positive or negative charge placed in a specified field.

❒  (5) Interpret an electric field diagram.

❒  (6) Analyze the motion of a particle of specified charge and mass in a uniform electric field.

b) Students should understand the concept of electric potential, so they can:

❒  (1) Determine the electric potential in the vicinity of one or more point charges.

❒  (2) Calculate the electrical work done on a charge or use conservation of energy to determine the speed of a charge that moves through a specified potential difference.

❒  (3) Determine the direction and approximate magnitude of the electric field at various positions given a sketch of equipotentials.

❒  (4) Calculate the potential difference between two points in a uniform electric field, and state which point is at the higher potential.

❒  (5) Calculate how much work is required to move a test charge from one location to another in the field of fixed point charges.

❒  (6) Calculate the electrostatic potential energy of a system of two or more point charges, and calculate how much work is required to establish the charge system.

❒  (7) Use integration to determine electric potential difference between two points on a line, given electric field strength as a function of position along that line.

❒  (8) State the general relationship between field and potential, and define and apply the concept of a conservative electric field.

3. Gauss’s law

a) Students should understand the relationship between electric field and electric flux, so they can:

❒  (1) Calculate the flux of an electric field through an arbitrary surface or of a field uniform in magnitude over a Gaussian surface and perpendicular to it.

❒  (2) Calculate the flux of the electric field through a rectangle when the field is perpendicular to the rectangle and a function of one coordinate only.

❒  (3) State and apply the relationship between flux and lines of force.

b) Students should understand Gauss’s Law, so they can:

❒  (1) State the law in integral form, and apply it qualitatively to relate flux and electric charge for a specified surface.

❒  (2) Apply the law, along with symmetry arguments, to determine the electric field for a planar, spherical or cylindrically symmetric charge distribution.

❒  (3) Apply the law to determine the charge density or total charge on a surface in terms of the electric field near the surface.

4. Fields and potentials of other charge distributions

a) Students should be able to use the principle of superposition to calculate by integration:

❒  (1) The electric field of a straight, uniformly charged wire.

❒  (2) The electric field and potential on the axis of a thin ring of charge, or at the center of a circular arc of charge.

❒  (3) The electric potential on the axis of a uniformly charged disk.

b) Students should know the fields of highly symmetric charge distributions, so they can:

❒  (1) Identify situations in which the direction of the electric field produced by a charge distribution can be deduced from symmetry considerations.

(2) Describe qualitatively the patterns and variation with distance of the electric field of:

❒  (a) Oppositely-charged parallel plates.

❒  (b) A long, uniformly-charged wire, or thin cylindrical or spherical shell.

❒  (3) Use superposition to determine the fields of parallel charged planes, coaxial cylinders or concentric spheres.

❒  (4) Derive expressions for electric potential as a function of position in the above cases.

B. Conductors, capacitors, dielectrics  (14%)

1. Electrostatics with conductors

a) Students should understand the nature of electric fields in and around conductors, so they can:

❒  (1) Explain the mechanics responsible for the absence of electric field inside a conductor, and know that all excess charge must reside on the surface of the conductor.

❒  (2) Explain why a conductor must be an equipotential, and apply this principle in analyzing what happens when conductors are connected by wires.

❒  (3) Show that all excess charge on a conductor must reside on its surface and that the field outside the conductor must be perpendicular to the surface.

❒  b) Students should be able to describe and sketch a graph of the electric field and potential inside and outside a charged conducting sphere.

c) Students should understand induced charge and electrostatic shielding, so they can:

❒  (1) Describe the process of charging by induction.

❒  (2) Explain why a neutral conductor is attracted to a charged object.

❒  (3) Explain why there can be no electric field in a charge-free region completely surrounded by a single conductor, and recognize consequences of this result.

❒  (4) Explain why the electric field outside a closed conducting surface cannot depend on the precise location of charge in the space enclosed by the conductor, and identify consequences of this result.

2. Capacitors

a) Students should understand the definition and function of capacitance, so they can:

❒  (1) Relate stored charge and voltage for a capacitor.

❒  (2) Relate voltage, charge and stored energy for a capacitor.

❒  (3) Recognize situations in which energy stored in a capacitor is converted to other forms.

b) Students should understand the physics of the parallel-plate capacitor, so they can:

❒  (1) Describe the electric field inside the capacitor, and relate the strength of this field to the potential difference between the plates and the plate separation.

❒  (2) Relate the electric field to the density of the charge on the plates.

❒  (3) Derive an expression for the capacitance of a parallel-plate capacitor.

❒  (4) Determine how changes in dimension will affect the value of the capacitance.

❒  (5) Derive and apply expressions for the energy stored in a parallel-plate capacitor and for the energy density in the field between the plates.

❒  (6) Analyze situations in which capacitor plates are moved apart or moved closer together, or in which a conducting slab is inserted between capacitor plates, either with a battery connected between the plates or with the charge on the plates held fixed.

c) Students should understand cylindrical and spherical capacitors, so they can:

❒  (1) Describe the electric field inside each.

❒  (2) Derive an expression for the capacitance of each.

3. Dielectrics

Students should understand the behavior of dielectrics, so they can:

❒  a) Describe how the insertion of a dielectric between the plates of a charged parallel plate capacitor affects its capacitance and the field strength and voltage between the plates.

❒  b) Analyze situations in which a dielectric slab is inserted between the plates of a capacitor.

C. Electric circuits   (20%)

1. Current, resistance, power

❒  a) Students should understand the definition of electric current, so they can relate the magnitude and direction of the current to the rate of flow of positive and negative charge.

b) Students should understand conductivity, resistivity and resistance, so they can:

❒  (1) Relate current and voltage for a resistor.

❒  (2) Write the relationship between electric field strength and current density in a conductor, and describe, in terms of the drift velocity of electrons, why such a relationship is plausible.

❒  (3) Describe how the resistance of a resistor depends upon its length and crosssectional area, and apply this result in comparing current flow in resistors of different material or different geometry.

❒  (4) Derive an expression for the resistance of a resistor of uniform cross-section in terms of its dimensions and the resistivity of the material from which it is constructed.

❒  (5) Derive expressions that relate the current, voltage and resistance to the rate at which heat is produced when current passes through a resistor.

❒  (6) Apply the relationships for the rate of heat production in a resistor.

2. Steady-state direct current circuits with batteries and resistors only

a) Students should understand the behavior of series and parallel combinations of resistors, so they can:

❒  (1) Identify on a circuit diagram whether resistors are in series or in parallel.

❒  (2) Determine the ratio of the voltages across resistors connected in series or the ratio of the currents through resistors connected in parallel.

❒  (3) Calculate the equivalent resistance of a network of resistors that can be broken down into series and parallel combinations.

❒  (4) Calculate the voltage, current and power dissipation for any resistor in such a network of resistors connected to a single power supply.

❒  (5) Design a simple series-parallel circuit that produces a given current through and potential difference across one specified component, and draw a diagram for the circuit using conventional symbols.

b) Students should understand the properties of ideal and real batteries, so they can:

❒  (1) Calculate the terminal voltage of a battery of specified emf and internal resistance from which a known current is flowing.

❒  (2) Calculate the rate at which a battery is supplying energy to a circuit or is being charged up by a circuit.

c) Students should be able to apply Ohm’s law and Kirchhoff’s rules to direct-current circuits, in order to:

❒  (1) Determine a single unknown current, voltage or resistance.

❒  (2) Set up and solve simultaneous equations to determine two unknown currents.

d) Students should understand the properties of voltmeters and ammeters, so they can:

❒  (1) State whether the resistance of each is high or low.

❒  (2) Identify or show correct methods of connecting meters into circuits in order to measure voltage or current.

❒  (3) Assess qualitatively the effect of finite meter resistance on a circuit into which these meters are connected.

3. Capacitors in circuits

a) Students should understand the t = 0 and steady-state behavior of capacitors connected in series or in parallel, so they can:

❒  (1) Calculate the equivalent capacitance of a series or parallel combination.

❒  (2) Describe how stored charge is divided between capacitors connected in parallel.

❒  (3) Determine the ratio of voltages for capacitors connected in series.

❒  (4) Calculate the voltage or stored charge, under steady-state conditions, for a capacitor connected to a circuit consisting of a battery and resistors.

b) Students should understand the discharging or charging of a capacitor through a resistor, so they can:

❒  (1) Calculate and interpret the time constant of the circuit.

❒  (2) Sketch or identify graphs of stored charge or voltage for the capacitor, or of current or voltage for the resistor, and indicate on the graph the significance of the time constant.

❒  (3) Write expressions to describe the time dependence of the stored charge or voltage for the capacitor, or of the current or voltage for the resistor.

❒  (4) Analyze the behavior of circuits containing several capacitors and resistors, including analyzing or sketching graphs that correctly indicate how voltages and currents vary with time.

D. Magnetic Fields (20%)

1. Forces on moving charges in magnetic fields

Students should understand the force experienced by a charged particle in a magnetic field, so they can:

❒  a) Calculate the magnitude and direction of the force in terms of q, v, and B, and explain why the magnetic force can perform no work.

❒  b) Deduce the direction of a magnetic field from information about the forces experienced by charged particles moving through that field.

❒  c) Describe the paths of charged particles moving in uniform magnetic fields.

❒  d) Derive and apply the formula for the radius of the circular path of a charge that moves perpendicular to a uniform magnetic field.

❒  e) Describe under what conditions particles will move with constant velocity through crossed electric and magnetic fields.

2. Forces on current-carrying wires in magnetic fields

Students should understand the force exerted on a current-carrying wire in a magnetic field, so they can:

❒  a) Calculate the magnitude and direction of the force on a straight segment of current carrying wire in a uniform magnetic field.

❒  b) Indicate the direction of magnetic forces on a current-carrying loop of wire in a magnetic field, and determine how the loop will tend to rotate as a consequence of these forces.

❒  c) Calculate the magnitude and direction of the torque experienced by a rectangular loop of wire carrying a current in a magnetic field.

3. Fields of long current-carrying wires

Students should understand the magnetic field produced by a long straight currentcarrying wire, so they can:

❒  a) Calculate the magnitude and direction of the field at a point in the vicinity of such a wire.

❒  b) Use superposition to determine the magnetic field produced by two long wires.

❒  c) Calculate the force of attraction or repulsion between two long current-carrying wires.

4. Biot-Savart law and Ampere’s law

a) Students should understand the Biot-Savart Law, so they can:

❒  (1) Deduce the magnitude and direction of the contribution to the magnetic field made by a short straight segment of current-carrying wire.

❒  (2) Derive and apply the expression for the magnitude of B on the axis of a circular loop of current.

b) Students should understand the statement and application of Ampere’s Law in integral form, so they can:

❒  (1) State the law precisely.

❒  (2) Use Ampere’s law, plus symmetry arguments and the right-hand rule, to relate magnetic field strength to current for planar or cylindrical symmetries.

❒  c) Students should be able to apply the superposition principle so they can determine the magnetic field produced by combinations of the configurations listed above.

E. Electromagnetism (16%)

1. Electromagnetic induction (including Faraday’s law and Lenz’s law)

a) Students should understand the concept of magnetic flux, so they can:

❒  (1) Calculate the flux of a uniform magnetic field through a loop of arbitrary orientation.

❒  (2) Use integration to calculate the flux of a non-uniform magnetic field, whose magnitude is a function of one coordinate, through a rectangular loop perpendicular to the field.

b) Students should understand Faraday’s law and Lenz’s law, so they can:

❒  (1) Recognize situations in which changing flux through a loop will cause an induced emf or current in the loop.

❒  (2) Calculate the magnitude and direction of the induced emf and current in a loop of wire or a conducting bar under the following conditions:

❒  (a) The magnitude of a related quantity such as magnetic field or area of the loop is changing at a constant rate.

❒  (b) The magnitude of a related quantity such as magnetic field or area of the loop is a specified non-linear function of time.

❒  c) Students should be able to analyze the forces that act on induced currents so they can determine the mechanical consequences of those forces.

2. Inductance (including LR and LC circuits)

a) Students should understand the concept of inductance, so they can:

❒  (1) Calculate the magnitude and sense of the emf in an inductor through which a specified changing current is flowing.

❒  (2) Derive and apply the expression for the self-inductance of a long solenoid.

b) Students should understand the transient and steady state behavior of DC circuits containing resistors and inductors, so they can:

❒  (1) Apply Kirchhoff’s rules to a simple LR series circuit to obtain a differential equation for the current as a function of time.

❒  (2) Solve the differential equation obtained in (1) for the current as a function of time through the battery, using separation of variables.

❒  (3) Calculate the initial transient currents and final steady state currents through any part of a simple series and parallel circuit containing an inductor and one or more resistors.

❒  (4) Sketch graphs of the current through or voltage across the resistors or inductor in a simple series and parallel circuit.

❒  (5) Calculate the rate of change of current in the inductor as a function of time.

❒  (6) Calculate the energy stored in an inductor that has a steady current flowing through it.

3. Maxwell’s equations

❒  Students should be familiar with Maxwell’s equations so they can associate each equation with its implications.

LABORATORY AND EXPERIMENTAL SITUATIONS

These objectives overlay the content objectives, and are assessed in the context of those objectives.

1. Design experiments

Students should understand the process of designing experiments, so they can:

❒  a) Describe the purpose of an experiment or a problem to be investigated.

❒  b) Identify equipment needed and describe how it is to be used.

❒  c) Draw a diagram or provide a description of an experimental setup.

❒  d) Describe procedures to be used, including controls and measurements to be taken.

2. Observe and measure real phenomena

❒  Students should be able to make relevant observations, and be able to take measurements with a variety of instruments (cannot be assessed via paper-and-pencil examinations).

3. Analyze data

Students should understand how to analyze data, so they can:

❒  a) Display data in graphical or tabular form.

❒  b) Fit lines and curves to data points in graphs.

❒  c) Perform calculations with data.

❒  d) Make extrapolations and interpolations from data.

4. Analyze errors

Students should understand measurement and experimental error, so they can:

❒  a) Identify sources of error and how they propagate.

❒  b) Estimate magnitude and direction of errors.

❒  c) Determine significant digits.

❒  d) Identify ways to reduce error.

5. Communicate results

Students should understand how to summarize and communicate results, so they can:

❒  a) Draw inferences and conclusions from experimental data.

❒  b) Suggest ways to improve experiment.

❒  c) Propose questions for further study.