The superposition principle holds for electromagnetic waves just as for electric and magnetic fields. Electromagnetic waves can be reflected off the surface of a conductor or a dielectric. The superposition of an incident wave and a reflected wave forms a standing wave. Suppose a sheet of a perfect conductor (zero resistivity) is placed in the yz-plane and a linearly polarized …
In a region of empty space where $\vec{E}$ and $\vec{B}$ fields are present, the total energy density $u$ is given by: $$u = \frac{1}{2} \epsilon_{0} E^{2} + \frac{1}{2 \mu_{0}} B^{2}$$ For electromagnetic waves in a vacuum, $$\begin{aligned} B &= \frac{E}{c} \\ &= \sqrt{\epsilon_{0} \mu_{0}} E \end{aligned}$$ It follows that: $$u = \epsilon_{0} E^{2}$$ In a vacuum, the energy density associated …
Every accelerated charge radiates electromagnetic energy – electromagnetic waves. Electric and magnetic disturbances radiate away from the source. Electromagnetic waves require no medium. (What’s “waving” in an electromagnetic wave are the time-varying electric and magnetic fields. The wave travels in vacuum with a definite and unchanging speed $c$ – the speed of light. Hertz produced pulses of electromagnetic radiation by generating …
Resonance In A.C. Circuits Suppose we connect an A.C. source with constant voltage amplitude V but adjustable angular frequency $\omega$ across an L-R-C series circuit. The current that appears in the circuit has the same angular frequency $\omega$ as the source and a current amplitude $I = \frac{V}{Z}$, where the impedance of the L-R-C series circuit is $Z = \sqrt{R^{2} …
Consider a series circuit containing a resistor R, an inductor L, and a capacitor C, through which there is a sinusoidal current, $i = I \cos{\omega t}$. We will consider the steady-state condition. We will look at the voltage across resistor: $$\begin{aligned} v_{R} &= iR \\ &= IR \cos{\omega t} \\ &= V_{R} \cos{\omega t} \end{aligned}$$ Voltage across inductor: $$\begin{aligned} …
This section deals with Mechanics at a level slightly higher than pre-university and is tailored towards first year Physics majors. This is a very simple introduction to Classical Mechanics. Basics Kinematics Newton’s Law Of Motion Work & Energy: Linear Momentum: Centre Of Mass Rotation Derivation Of Moment Of Inertia Of Common Shapes: Rotational Dynamics Angular Momentum To Be Added: – Static Equilibrium …
Resistor In An A.C. Circuit Consider a resistor with resistance R through which there is a sinusoidal current: $$i = I \cos{\omega t}$$ From Ohm’s Law, $$\begin{aligned} v_{R} &= iR \\ &= \left( IR \right) \cos{\omega t} \\ &= V_{R} \cos{\omega t} \end{aligned}$$ The current $i$ is in phase with the voltage $v_{R}$ The instantaneous power $p$ delivered to a …