## Romulans, Klingons and Earth

Being at quarrel since over two centuries, Romulans and Klingons have decided that it is now time to settle their differences once and for all. They have sent their admiral… Click here to read more

Physics tutorials, questions and answers

This site was started back in 2008, and features, among others, a collection of physics homework exercises and tutorials for all levels of physics students (high school and college).

We hope our site will help you advance in your studies and make it easier to understand physics, hence the world that surrounds us!

All the contents of this site were written by Valentin Bogatu (Physics, PhD).

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Being at quarrel since over two centuries, Romulans and Klingons have decided that it is now time to settle their differences once and for all. They have sent their admiral… Click here to read more

You are given a current source made of a NPN transistor, having $I_c=1 mA$ and $beta=100$. the purpose of the diodes is to create a constant voltage drop ($0.45 V$)… Click here to read more

Inside the Sun the average temperature is $10^7 K$. For Hydrogen atoms the ground state $E_1=-13.6 eV$ (1S) has degeneracy one, and the first excited state has degeneracy 4 $E_2=-13.6/4=-3.4… Click here to read more

Prove the following a) Let $(\hat e_1,\hat e_2. \hat e_3)$ be the unit vectors of a right handed, orthogonal coordinate system. Demonstrate that Levi-Civita symbol satisfies $\epsilon_{ijk} =\hat e_i(\hat e_j… Click here to read more

1. The wave function of a particle in a ring is $psi(phi,t)=frac{1}{sqrt{2pi}}frac{1}{sqrt{2}}e^{-iphi}e^{ihbar t/2I}-frac{1}{sqrt{2pi}}frac{1}{sqrt{2}}e^{-iphi}e^{i2hbar t/2I}$. Please find the expectation value of the energy. $psi=frac{1}{sqrt{2pi}}(C_1phi_1+C_2phi_2)$ is a mix of elementary states. For… Click here to read more

You are given a rod having a linear mass density $\lambda(x) =\frac{2M}{2L}[1+(x/L)]$. Then you place a donut (as a cylinder) at a distance $d=0.75L$ from the lighter end, having a… Click here to read more

For testing a bridge, there are used four strain gauges ($R_1-R_4$) glued to it. The bridge is made of 30 ft. long I beams, each having a height of 3… Click here to read more

You are given a particle that is in the ground state of the quantum mechanical infinite square well of width $a$. Suddenly you increase the size of the square well… Click here to read more

A rectangular prism has width $a$, height $b$ and length $c$ as show at right. a) What general type of function should you use to find a solution of the… Click here to read more

For the given function $\phi(r)=1/r=1/\sqrt{x^2+y^2+z^2}$ demonstrate that $\nabla^2\phi(r)=0$ on $\Re\setminus{0}$ and that the function itself tends to zero when each $x,y,z->\infty$ $\phi=\frac{1}{\sqrt{x^2+y^2+z^2}}$ $\frac{d\phi}{dx}=-\frac{2x}{2(x^2+y^2+z^2)^{3/2}}=-\frac{x}{(x^2+y^2+z^2)^{3/2}}$ ,$\frac{d\phi}{dy}=-\frac{y}{(x^2+y^2+z^2)^{3/2}}$ and $\frac{d\phi}{dz}=-\frac{z}{(x^2+y^2+z^2)^{3/2}}$ $\frac{d^2\phi}{dx^2}=-\frac{1}{(x^2+y^2+z^2)^{3/2}} +(3/2)*\frac{2x^2}{(x^2+y^2+z^2)^{5/2}}=-\frac{1}{(x^2+y^2+z^2)^{3/2}}+\frac{3x^2}{(x^2+y^2+z^2)^{5/2}}$ $\frac{d^2\phi}{dy^2}=-\frac{1}{(x^2+y^2+z^2)^{3/2}}+\frac{3y^2}{(x^2+y^2+z^2)^{5/2}}$ $\frac{d^2\phi}{dy^2}=-\frac{1}{(x^2+y^2+z^2)^{3/2}}+\frac{3z^2}{(x^2+y^2+z^2)^{5/2}}$… Click here to read more

Please find L, S, and J for the following different atoms using Hund’s and Aufbau principles 1. Sulfur (S) Z= 16 2. Vanadium (V), Z = 23 3. Zirconium (Zr),… Click here to read more

You are given the dual cycle from the figure with the following data: compression ratio 1:15, $P_1=14.4 PSI$, $T_1=60 F$. The volume ratio $V_4/V_3=2:1$ and the pressure ratio $P_3/P_2=1.5:1$. You… Click here to read more

Introduction At the end of 1800 years, more precisely around 1887 a renowned German physicist (we know today his name from the measuring unit of frequency) H.R. Hertz, performed for… Click here to read more

1. (a) Please explain why some atoms are paramagnetic and others are diamagnetic. (b) Define Ferromagnetism, Antiferromagnetism, Ferrimagnetism, and Itinerant Ferromagnetism. a) $M=χH$ ($M$ is magnetization, $H$ is magnetic… Click here to read more

Consider a dilute gas of diatomic molecules where the beginning and the end of the molecules are different, such as $H-D$ (Hydrogen-Deuterium) molecules. We focus here on the rotational degrees… Click here to read more

Consider a particle of mass $m$ in the infinite square well of width $L$. Its initial wave function (at time $t=0$) is a coherent mixture of the second and third… Click here to read more

You are given a capacitor with the surface area $S$ having distance between the armatures $d$. The capacitor is charged with surface densities $\pm\sigma$ and the the voltage source is disconnected…. Click here to read more

What is the potential of the infinite slot from Griffiths 3.3, if you are given a varying potential $V(0,y)=V_0x/a$ as a boundary condition at $x=0$ For the given arrangement of… Click here to read more

For the spherically symmetric charge distribution located in free space, having $\rho=\left\{\begin{matrix}3r^2&\text{ for r<a}\\\rho=0&\text{ for r>a}\end{matrix}\right.$a) Use the potential definition and integrate the charge distribution to find the potential at… Click here to read more

For the asymmetric quantum well in the figure please find the first two bound states and energies. prove that it is possible for an asymmetrical well to have no bound… Click here to read more