The mathematics underlying LCR circuit theory for AC currents is discussed. Complex numbers are used to convert differential equations to algebraic equations. The notion of impedance is introduced. The radio is used to illustrate the concepts of resonance and variable capacitance. The body of classical electromagnetism treated so far is reviewed and summarized. The displacement current is introduced, leading to the complete Maxwell equations.
Like capacitors, inductors act as energy storage devices in circuits. The relationship between voltage, inductance and current in a variety of circuits with DC voltages is described.
The electric effect of a changing magnetic field is described using Faraday’s Law. The direction of the current so generated is given by Lenz’s Law. The operation and energy accounting of the generator are described. The concept of inductance is introduced. The Betatron is described as an example of Faraday’s Law. Self and mutual inductance are introduced. The energy density in a magnetic field is derived.
Ampere’s Law is used to find the magnetic field generated by currents in highly symmetric geometries like the infinitely long wire and the solenoid. It is shown how magnetism can be used to convert macroscopic mechanical energy to do microscopic electrical work. Lenz’s and Faraday’s Laws are introduced. The latter says that a changing magnetic field generates a non-conservative electric field.
The mechanism by which electric currents produce a magnetic field (Law of Biot-Savart) is discussed in greater detail. The field due to a single loop and an infinite wire are computed. Ampere’s Law is derived. The operation of the DC electric motor is used to illustrate the torque generated on moving charges in a magnetic field.
After a description of more complicated electric circuits, the basic ideas underlying magnetism are discussed and the relationship between electrical charges and magnetic fields is explored. Magnetism is caused and experienced only by moving charges. The Lorentz force on a charge is described and used to deduce the force on a current carrying wire. The cyclotron and velocity selector are described.
The lecture begins with a discussion of electric potential distribution in conductors. Image charges are introduced and exploited. Capacitance is explained in greater detail and illustrated using the parallel plate capacitor. The energy stored in the electric field is derived. The forces acting on an electric current flowing through a conducting wire are examined. The RC circuits and its energetics are discussed. The EMF due to a battery is explained.
The electric potential is defined for the electric field. It is introduced as an integral of the electric field making the field the derivative of the potential. After discussing the ideas of electric potential and field as presented in the previous lecture, the concept of capacitance is introduced as a means of storing charge and energy.
The law of conservation of energy is reviewed using examples drawn from Newtonian mechanics. The work-energy theorem is derived from first principles and used to initiate a discussion of the vector calculus underlying the law of conservation of energy.
Lecture begins with a recap of Gauss’s Law, its derivation, its limitation and its applications in deriving the electric field of several symmetric geometries—like the infinitely long wire. The electrical properties of conductors and insulators are discussed. Multiple integrals are briefly reviewed.
