## Spherical shell potential (Griffiths)

The charged sphere A spherical shell has spherical symmetry and because of this we write its potential as $V(R,\theta)=V_0(\theta)$ ($\theta$ is the “polar” angle of the spherical coordinate system). a) When $V_0(\theta)=V_0(1-\theta^2)$ find the equation of definition for $V(R,\theta)$ if $r>R$. b) When $V_0(\theta)=V_0(\cos^2 \theta +2)$ please evaluate the potential of this spherical shell at

## Simple Tunneling

Electron wave An electron travels toward negative values of $x$ having a kinetic energy $E=2 eV$. Please write the equation of this electron wave and describe its characteristic values. The general equation of the wave travelling in the negative x direction (towards left) is $\psi(x,t)=A\exp[i(kx+\omega t)]$  ($A$ is the wave amplitude) For a fixed point

## Step Down Potential (Griffiths)

Find the reflection coefficient of a plane wave with energy $E>V$ on a “step potential” initially 0 that drops down to $-V_0$. How is this similar and different to a classical particle?  Consider a plane wave coming from the left towards the step. Since $E>0$ it is a wave that has two components: incoming component

## Cylinder with Uniform Current

For a uniform current that goes through a long cylinder (z-axis) please find a) force exerted by the upper half on the lower half of the cylinder. b) magnitude of this force for cylinder length of 1 meter, diameter of 1 mm and current of 10 A.  The current density inside the wire is$j=I/S=I/(πa^2)$Consider first the