# PHYS 212 Study Guide - Final Guide: Inductor, Plane Wave, Harmonic Oscillator

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Published on 19 Apr 2015

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PHYS 212- Spring 2014

Exam #1- Review Sheet

Questions & Corrections: Hassan Shapourian (hassan88@illinois.edu)

General tip

Be careful about units in Electromagnetism. Often prefixes are used as there are small or large quantities.

Always convert prefixes back to the base unit before using them mathematically. Sometimes you can find

the correct choice by checking the signs/dimensions/limiting behavior.

Vectors

Vectors are shown by arrows. The length of arrow is proportional to the magnitude of vector. Vectors can be

projected into their components

Add vectors component by component:

Coulomb’s Law

The electric force between two point charges and is given by

Note that this has a similar form to the gravitation force between two masses, however, it can be either repulsive or

attractive (like charges repel, unlike charges attract each other).

Use superposition principle to compute the net force on charge q due to , , ….

Be careful here, you are adding vectors!

Electric Field

The electric field summarizes the influence of a collection of charges on any “test charge” q that we place in their

vicinity.

And for the example above it is going to be

PHYS 212- Spring 2014

Exam #1- Review Sheet

Questions & Corrections: Hassan Shapourian (hassan88@illinois.edu)

Notice that electric field is a property that we assign to the space surrounding a collection of charges. So, it doesn’t

depend on the test charge. Electric field is a vector field denoted by

; i.e. it has magnitude and direction at every

point of the space.

Electric field lines: a graphical representation of

following these rules

Field lines originate from positive charges and end on negative charges

Field lines are continuous and never cross (except at the position of point charges)

The number of field lines connected to a charge is proportional to that charge’s magnitude.

Important result of field lines representation:

The electric field is stronger where the field lines are denser.

Note that what matters is the density of field lines, being on a field line itself doesn’t imply a stronger field!

Mechanical Equilibrium

A system is said to be in equilbirum where the net forcce on it vanishes. There are three types of equilibria:

Stable equilibrium: in this situation, once the system is slightly disturbed from equilibrium point, it

experiences a restoring force and meets the equilibrium point periodically. Generally, this case can be

demonstrated by a potential energy and force as in

Unstable equilibrium: here, if the system is disturbed, it moves away from the equilibrium point. Not

only is there no restoring force, but also the force tends to push the particle away.

Indifferent equilibrium: the system is indifferent to any perturbation.

The fastest way to determine the type of equilibrium is to displace the particle from it equilibirum position and find

the dominant force.

Gauss’ Law

Electric flux: the total field strength passing through a given surface. In a fluidic system, it would be net amount

of fluid passing through a surface per unit time.

PHYS 212- Spring 2014

Exam #1- Review Sheet

Questions & Corrections: Hassan Shapourian (hassan88@illinois.edu)

where

is directed normal to the element of area with magnitude equal to area of that element. In

case of uniform field on flat surface, it is simplified into .

Statement of Gauss’ law: the total electric flux through any closed surface is propotional to the total

amount of charge enclosed by that surface.

Note that

is always directed outward for a closed surface.

Application of Gauss’ law: We can use Gauss’ law to compute the electric field for some symmetric chage

distributions. Here is a four-step procedure to do this:

Sketch the electric field lines using all the symmetries of the problem.

Choose a suitable Gaussian surface based on the geometry of the problem.

Determine the total charge enclosed by your surface.

Evaluate the flux integral and combine it with Gauss’ law to determine

.

Examples:

Solid sphere

Charge is uniformly distributed over a sphere with density . The outside field ( ) is similar to a point

charge sitting at the origin.

Also, the inside field ( ) is

Solid infinite cylinder