effective charge

Effective Charge Laboratory

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

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

Sled

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

Inertia

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

bridge

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

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

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