Learning Outcomes - PHYS 2015 Electric charges and forces: Describe the electrical nature of matter; Explain how an object can be charged; Distinguish between electrical conductors and insulators and the motion of charges in each; Apply the conservation of charge. Describe qualitatively the properties of the electric force and Coulomb s law; Interpret the forces present in various charge configurations, including those where polarization or electric dipoles are involved. Evaluate quantitatively via Coulomb s law electric forces as vectors for a pair of charges, for multiple point charges, and charge distributions acting on a point charge. Electric fields: Explain the concept of the electric field and relate it to electric forces; Interpret and construct electric field line patterns in terms of the source charges; Describe the effects of an electric field on a test charge. Calculate as a vector the electric field that is produced by a collection of point charges; Interpret and apply the concepts of volume, surface and line charge densities to calculate via integration the electric field vector produced by continuous charge densities. Describe the forces and torques exerted on an electric dipole in a field. Electric Flux and Gauss s law: Represent area as a vector Define electric flux Determine the flux through a flat surface, including situations where the normal vector is not parallel to field Explain what a Gaussian surface is; Recognize when Gauss s law is useful for a calculation of electric field and articulate the symmetry of the electric field; Apply Gauss s law to appropriate problems to find electric field for situations of spherical, cylindrical (linear) or plane symmetry; Apply Gauss s law to explain or determine charge distributions on conductors in equilibrium.
Electric potential and potential energy: Apply the definition of work to a charge moving in an electric field to find the work done by the electric force on the charge, including recognizing the sign associated with the work and determine the associated changes in kinetic and potential energies; Evaluate the electric potential energy of a system of two or more point charges. Determine the scalar electric potential of a source charge and charge distributions. Describe qualitatively the motion of positive or negative charges in a region of space given the electric potential. Use the electric potential due to a source to evaluate changes in potential and kinetic energies Find the change in potential between two locations from a given electric field and find the electric field from a given electric potential function. Explain the difference between U and V. Explain the significance of equipotential surfaces. Relate electric field line patterns to the associated equipotential lines or surfaces. Capacitance and capacitors: Define capacitance and explain the primary function of a capacitor; Relate capacitance to the geometry of the capacitor, particularly parallel plate and coaxial geometries; Explain the distinction between series and parallel capacitors in terms of charge stored and potential drops in each case; Determine an equivalent capacitance of some combination of capacitors in parallel and series. Explain the purpose of a battery in a circuit and the idea of EMF. Explain how energy is stored by a capacitor and determine how much energy is stored in a given capacitor/set of capacitors Describe how a dielectric affects capacitance. Reason about relationships among potential difference, field, charge and stored energy in a capacitor. Circuits: currents and resistance: Define and calculate current and current density; Describe the microscopic model of conduction; relating drift velocity to electric field and current density, and potential differences to electric fields in conductors; Explain the meaning of conductivity and resistivity (and their temperature dependence) and their relationship to resistance; Apply Ohm s law to determine the current through a material with a resistance and a potential difference across it; Calculate the power dissipated in a resistor. Identify when resistors are arranged in series or parallel; State Kirchhoff s rules and apply to a multi-branch circuit;
Simplify networks of resistors to their equivalent resistance; Evaluate the currents through, potential drops across, and power dissipated in individual resistors in a multi-element circuit; Predict qualitatively what changes occur in a circuit if one or more components is altered; Describe the time dependence of voltages and currents present in RC circuits; Apply the equations describing currents and voltages in RC circuits. Magnetic Fields and Forces: Explain the origin of magnetic fields from moving charges, both at the atomic scale and from electric currents in wires. Describe and sketch magnetic field lines arising from long wires and magnetic dipoles/permanent magnets. Apply the Biot-Savart law and the right-hand rule to evaluate the direction of the magnetic field from a current segment and to calculate the magnetic field for simple current configurations (loop, long wire). Add the magnetic fields arising from combinations of wires as vectors to find the net magnetic field (magnitude and direction) at a point. Calculate the magnetic force on an electric charge moving through a magnetic field and describe the resulting motion, including circular motion in a uniform field. Describe and calculate the path taken by a charged particle traveling through crossed electric and magnetic fields, as in a velocity selector or in the Hall effect. Evaluate the force on current carrying wires in a magnetic field, including parallel wires carrying currents. Define the magnetic dipole moment of a current loop. Evaluate the forces and torques on a current loop or magnetic dipole and describe the resulting motion. Apply these ideas to explain the operation of an electric motor. Calculate the magnetic potential energy of a magnetic dipole in a magnetic field. State and use Ampere s law, including identifying current distributions with sufficient symmetry for its use, choosing a path to use Ampere s law, and calculating the magnetic field. Distinguish between the magnetic fields of wires, solenoids, toroids, and sheets of current. Define and calculate magnetic flux. State Gauss s law for magnetic fields. Explain its significance in terms of magnetic monopoles. Electromagnetic induction, Maxwell s equations: State Faraday s law and identify situations for which magnetic flux or flux linkage is changing. Use Faraday s law to calculate induced EMFs for situations with time-varying magnetic fields Calculate motional EMFs for conductors moving in magnetic fields.
Apply Lenz s law to identify the direction of induced currents and induced electric fields. Explain the operation of an electric generator using magnetic induction. Explain the operation of transformers. Describe the time dependence and calculate the currents and voltages in simple RL series circuits. Recognize Maxwell s equations (including Maxwell-Ampere s law with the inclusion of the displacement current. Recognize the wave equations for electric and magnetic fields that result from Maxwell s equations. Electromagnetic Waves: Interpret and apply the mathematical form for traveling waves, including relationships among wave number, wavelength, frequency, period, and angular frequency. Describe and illustrate the electric and magnetic fields of a linearly polarized traveling EM wave. Describe and use Malus Law to evaluate the effects of linear polarizers on unpolarized and polarized light. Evaluate where in the electromagnetic spectrum a wave falls. Use the Poynting vector, and distinguish between instantaneous and average power and intensity of an EM wave. Evaluate radiation forces and pressure. Geometric/Ray Optics: Apply the law of reflection to illustrate with ray-tracing image formation with plane, concave, and convex mirrors, and identify images as real or virtual. Apply the relationship between object and image distances and focal length to locate images or objects formed by mirrors, applying appropriate sign conventions. Define the index of refraction and explain its relationship to the speed of light. Explain the meaning of dispersion. Know and apply the law of refraction/snell s law to light passing between media; Sketch or evaluate possible ray paths at interfaces. Define the critical angle and evaluate whether or not total internal reflection will occur at an interface. Use the lens maker s equation to design thin lenses of desired focal lengths. Illustrate with ray-tracing image formation with converging and diverging lenses, and identify images as real or virtual. Apply the relationship between object and image distances and focal length to locate images or objects, applying appropriate sign conventions, for a single lens system. Locate images formed by a system with 2 lenses or a lens and mirror. Explain the operation of a simple magnifier, compound microscope, or telescope.
Physical/Wave Optics: Identify and apply the conditions for constructive and destructive interference of waves, relating path differences to phase differences, for two coherent point sources, including for the two-slit interference pattern and a diffraction grating. Incorporate phase changes on reflections to analyze conditions for constructive and destructive interference from thin films.