2. a nonzero current for a short instant. 3. a steady current. The primary coil of a transformer is connected to a battery, a resistor, and a switch. The secondary coil is connected to an ammeter. When the switch is thrown closed, the ammeter shows 1. zero current. 2. a nonzero current for a short instant. 3. a steady current. Answer: 2.When the switch is thrown closed, it momentarily produces a time-varying current in the primary coil of the transformer. The iron core then acts as an electromagnet and generates a transient current in the secondary coil via electromagnetic induction.

Application: Electrochemical Analysis of Surface Modifications Series combination of CH and CD gives the double layer capacitance (Cd) Capacitive layers formed due to presence of charged species near surface

Impedance of working electrode One additional branch for each reaction R – Resistance to interaction with surface C – Capacitance formed due to presence of charged species W – Impedance related to mass transfer The impedance at the surface can be resolved into several different types of elements

Electricity and Magnetism Optics

CH 31: Electromagnetic waves

We have discussed electromagnetic waves, which consists of several different categories. Radio waves, microwaves, infrared, visible, ultraviolet, x-rays and gamma rays. We are now going to focus specifically on the visible spectrum of light. Most of the topics we will discuss are also applicable to any category of electromagnetic wave. Electromagnetic waves (we will call it light from now on) travel in the form of waves and particles. We are going to discuss the wave properties of light now and you will be introduced to the particle nature of light later. Light travels in a straight line from the source. The path the light follows is typically drawn as a ray (line describing the direction of propagation of the light). Light will only change direction due to an interaction with a medium. There are several ways to change the direction of light and we will discuss each in turn.

Electromagnetic Waves Electromagnetic waves are identical to mechanical waves with the exception that they do not require a medium for transmission. The “medium” is the electric and magnetic fields that travel with the wave. The electric and magnetic fields are oscillating in time. What does an oscillating magnetic field cause? An oscillating electric field. What does an oscillating electric field cause? An oscillating magnetic field. This can all be described using Maxwell’s Equations The oscillating electric field and the oscillating magnetic field are always perpendicular to each other. They are also perpendicular to the direction of propagation of the wave.

We describe the motion (propagation and oscillation) of a wave using the wave equation. We will look at the wave equation for a plane electromagnetic wave. Plane wave – All waves from a single source are traveling in a single direction and all of the corresponding oscillations occur in a single plane perpendicular to the direction of propagation. Assumptions: 1) All waves are in phase. 2) All rays are parallel. 3) E and B are only functions of x and t. 4) E is in y-direction and B is in z-direction. 5) We are in empty space q = 0 and I = 0. The derivation of these equations is presented in the text, but will not be discussed here. Ray – line along which a wave propagates. We can now relate the electric field and the magnetic field. We want a single expression that includes either the magnetic field or the electric field. We can do this by first differentiating either of the two expressions shown with respect to x.

Similarly for B: Generalized Wave Equation: We can then obtain a solution to these second order differential equations. Define c in order to have a similar form. x – location along x-axis t – time w – angular frequency of oscillation k – angular wave number Wave speed equation