The definition of the effective charge In this paper we will determine the effective charge of an electron. The effective charge is by definition the ratio (e/m). Background Information and History Thomson was the first scientist that used a selection of different gases to determine the ratio of the electric charge of a particle to

## 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

## Icy slope and sled

The icy slope A frictionless icy slope of angle $\theta$ having a length $L$, followed by a horizontal portion, then by a bump ($R$) make a frictionless path as in the image. The weight of the sled on this path is C*TrueWeight when the sled is exactly at the bump’s top, ($0 < = C

## Moment of Inertia

Circle moment of inertia Find the principal moments of inertia of a circle of radius $R$ and mass $m$. Use the integration over the circle length. (Hint: first define the infinitesimal moment of inertia). The inertia moment is a measure of how a body that has certain dimensions, opposes to changes in rotation motion, exactly

## Wien Bridge

The Bridge In the figure is presented a Wien Bridge. When its two arms are at equilibrium ($R1*R3=R2*R4$) the voltage on the Wien bridge diagonal cancels. You apply to this bridge a voltage $V(t)=100*\cos(100 t)$ V and to you are using an oscilloscope with $R(in)=1M\Omega$. a) You determine the voltage between a) and b) directly.

## Analog-Digital Converter

The Analog-Digital Converter The input range of a 10 bit ADC varies from +0.1..+4.9V. a) What input step size has this analog-digital converter? b) For a full scale sine wave please find the SNR of its quantisation in dB. c) Find the number of bits for this ADC if the quantization SNR is 90 dB.

## Pendulum Lab. Interference

Pendulum Laboratory The equations of pendulum are $T= C * \sqrt{L/g}$ (1) $T= 2\pi * \sqrt{L/g} * [1+(1/2)^2*\sin^2(x/2)+(3/4)^2*\sin^4(x/2)]$ (2) 1. For which angle is the period given by pendulum equation (2) diferrent with 1% from that given by the simplest equation (1)? You can consider just the first and second term in the sum of