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Previously, we've learned about the electric field of a point particle. Often, when analyzing physical systems, it is the case that we're unable to analyze each individual particle that composes an object and need to therefore generalize collections of particles into shapes (in this case, a rod) whereby the mathematics corresponding to electric field calculations can be simplified. This can essentially be done by adding up the contributions to the electric field made by parts of an object, approximating each part of an object as a point charge.
Previously, we've learned about the electric field of a point particle. Often, when analyzing physical systems, it is the case that we're unable to analyze each individual particle that composes an object and need to therefore generalize collections of particles into shapes (in this case, a rod) whereby the mathematics corresponding to electric field calculations can be simplified. This can essentially be done by adding up the contributions to the electric field made by parts of an object, approximating each part of an object as a point charge.
=== The System in Question ===
As discussed in the previous section, we're considering a system
abstracted from the particle model we're familiar with, therefore we will
make the generalization that our rod of length L has a total charge of
quantity Q. For this generalization, we will need to assume that the rod
is so thin that we can ignore its thickness.
[image 1]
Since the electric field produced by a charge at any given location is
proportional to the distance from the charge to that location, we will
need to relate the observation location to the source of the charge, which
we will consider the origin of the rod. To do that, we will need to divide
the rod into pieces of length \delta y each containing a charge \delta Q.
In the image below, you can see what this looks like and the relation that
can be found between the observation location and the source, forming the
distance vector \vect{r}.
[image 2]
By the pythagorean theorem, we can find the vector \vect{r} as follows:
[image 3]
And to find the unit vector in the direction of \vect{r}, \hat{r}, we do as
follows:
[image 4]


===Week 5===
===Week 5===

Revision as of 23:36, 25 November 2018

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Physics 1

Week 1

Help with VPython

Vectors and Units

VPython

Vectors and Units

Interactions

Velocity and Momentum

Week 2

Momentum and the Momentum Principle

Iterative Prediction with a Constant Force

Week 3

Analytic Prediction with a Constant Force

Iterative Prediction with a Varying Force

Week 4

Fundamental Interactions

Week 5

Conservation of Momentum

Properties of Matter

Week 6

Identifying Forces

Curving Motion

Week 7

Energy Principle

Week 8

Work by Non-Constant Forces

Potential Energy

Week 9

Multiparticle Systems

Week 10

Choice of System

Thermal Energy, Dissipation, and Transfer of Energy

Rotational and Vibrational Energy

Week 11

Different Models of a System

Models of Friction

Week 12

Collisions

Week 13

Rotations

Angular Momentum

Week 14

Analyzing Motion with and without Torque

Week 15

Introduction to Quantum Concepts

Physics 2

Week 1

3D Vectors

Electric field

Electric force

Electric field of a point particle

Superposition

Dipoles

Week 2

Interactions of charged objects

Tape experiments

Polarization

Week 3

Insulators

Conductors

Charging and Discharging

Week 4

Physics 3

Week 1

Classical Physics

Week 2

Special Relativity

Week 3

Photons

Week 4

Matter Waves

Week 5

Wave Mechanics

Week 6

Rutherford-Bohr Model

Week 7

The Hydrogen Atom

Week 8

Many-Electron Atoms

Week 9

Molecules

Week 10

Statistical Physics

Week 11

Condensed Matter Physics

Week 12

The Nucleus

Week 13

Nuclear Physics

Week 14

Particle Physics

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