Course Objectives for Advanced Placement Physics C – Electricity and Magnetism

A. Electrostatics

1. Charge, Field, and Potential

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

(3) Calculate the net force and torque on a collection of charges in an electric field.

(4) Given a diagram on which an electric field is represented by flux lines, determine the direction of the field at a given point, identify locations where the field is strong and where it is weak, and identify where positive or negative charges must be present.

(5) 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) Calculate the electrical work done on a positive or negative charge that moves through a specified potential difference.

(2) Given a sketch of equipotentials for a charge configuration, determine the direction and approximate magnitude of the electric field at various positions.

(3) Apply conservation of energy to determine the speed of a charged particle that has been accelerated through a specified potential difference.

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

(5) Given electric field strength as a function of position along a line, use integration to determine electric potential as a function of position.

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

2. Coulomb’s Law and Field and Potential of Point Charges

a. Students should understand Coulomb’s Law and the principle of superposition so they can:

(1) Determine the force that acts between specified point charges, and describe the electric field of a single point charge.

(2) Use vector addition to determine the electric field produced by two or more point charges.

b. Students should know the potential function for a point charge so they can:

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

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

(3) Calculate the electrostatic potential energy of a system of two or more point charges, and calculate how much work is required to move a set of charges into a new configuration.

3. 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 of a thin ring of charge on the axis of the ring, or of a semicircle of charge at its center.

(3) The electric potential of a uniformly charged disk on the axis of the 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 the electric field of:

(a) Parallel charged plates.

(b) A long uniformly charged wire or thin cylindrical shell.

(c) A thin 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.

4. Gauss’s Law

a. Students should understand the relationship between field and flux so they can:

(1) Calculate the flux of a uniform electric field E through an arbitrary surface.

(2) Calculate the flux of E through a curved surface when E is uniform in magnitude and perpendicular to the surface.

(3) Calculate the flux of E through a rectangle when E is perpendicular to the rectangle and a function of one coordinate only.

(4) 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 near a large uniformly charged plane, inside or outside a uniformly charged long cylinder or cylindrical shell, and inside or outside a uniformly charged sphere or spherical shell.

(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) Graph the electric field and potential function by the calculus method of finding maxima and minima.

B. Conductors, Capacitors, Dielectrics

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 why 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 joined by wires.

(3) Determine the direction of the force on a charged particle brought near an uncharged or grounded conductor.

(4) Prove 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.

(5) Prove and apply the relationship between the surface charge density on a conductor and the electric field strength near its 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 qualitatively the process of charging by induction.

(2) Determine the direction of the force on a charged particle brought near an uncharged or grounded conductor.

(3) Explain qualitatively 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 qualitatively 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 and Dielectrics

a. Students should know the definition of capacitance so they can relate stored charge and voltage for a capacitor.

b. Students should understand energy storage in capacitors so they can:

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

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

c. 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) 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.

(6) Analyze situations in which a conducting or dielectric slab is inserted between the plates of a capacitor.

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

(8) 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.

d. 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.

C. Electric Circuits

1. Current, Resistance, Power

a. Students should understand the definition of electric current so they can relate the magnitude and direction of the current in a wire or ionized medium 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 qualitatively, 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 cross-sectional area.

(4) Derive an expression for the resistance of a resistor of uniform cross-section in terms of its dimensions and the conductivity of the material from which it is constructed, and apply this result in comparing current flow in resistors of different material or different geometry.

(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 resistors that 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 two or more resistors connected in series or in parallel, or 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 battery.

(5) Design a simple series-parallel circuit that produces a given current and terminal voltage for 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.

(3) State what external resistance draws maximum power from a battery of specified internal resistance, and apply this result in solving problems involving one or more resistors connected to a single battery.

c. Students should be able to apply Ohm’sLaw 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 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 two capacitors connected in parallel.

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

b. Students should understand energy storage in capacitors so they can:

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

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

c. Students should be able to calculate the voltage or stored charge, under steady-state conditions, for a capacitor connected to a circuit consisting of a battery and resistors.

d. 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.

e. Students should develop skill in analyzing the behavior of circuits containing several capacitors and resistors so they can:

(1) Determine voltages and currents immediately after a switch has been closed and also after steady-state conditions have been established.

(2) Identify graphs that correctly indicate how voltages and currents vary with time.

D. Magnetostatics

1. Forces on Moving Charges in Magnetic Fields

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

(1) Calculate the magnitude and direction of the force interms of q, v, and B, and explain why the magnetic force can perform no work.

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

(3) State and apply the formula for the radius of the circular path of a charge that moves perpendicular to a uniform magnetic field, and derive this formula from Newton’s Second Law and the magnetic force law.

(4) Describe the most general path possible for a charged particle moving in a uniform magnetic field, and describe the motion of a particle that enters a uniform magnetic field moving with specified initial velocity.

(5) Describe quantitatively under what conditions particles will move with constant velocity through crossed electric and magnetic fields.

2. Forces on Current-carrying Wires in Magnetic Fields

a. Students should understand the force experienced by a current in a magnetic field so they can:

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

(2) 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.

(3) 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

a. Students should understand the magnetic field produced by a long straight current-carrying wire so they can:

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

(2) Use superposition to determine the magnetic field produced by two long wires.

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

4. The 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 a long straight wire, or for a hollow or solid cylinder.

c. Students should develop skill in applying the superposition principle so they can determine the magnetic field produced by combinations of the configurations listed above.

E. Electromagnetism

1. Electromagnetic Induction

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 nonuniform 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) A square loop of wire pulled at a constant velocity into or out of a uniform magnetic field.

(b) General cases of a loop of wire that is being pulled into or out of a uniform magnetic field.

(c) A loop of wire placed in a spatially uniform magnetic field whose magnitude is changing at a constant rate.

(d) A loop of wire placed in a spatially uniform magnetic field whose magnitude is a specified function of time.

(e) A loop of wire that rotates at a constant rate about an axis perpendicular to a uniform magnetic field.

(f) A conducting bar moving perpendicular to a uniform magnetic field.

c. Students should develop skill in analyzing the forces that act on induced currents so they can solve simple problems involving the mechanical consequences of electromagnetic induction.

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 develop skill in analyzing circuits containing inductors and resistors so they can write and solve the differential equation that relates current to time.

3. Maxwell’s equations in integral form

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