### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# INTRO ELECTRICITY & MAGNETISM PHYS 260

WKU

GPA 3.72

### View Full Document

## 7

## 0

## Popular in Course

## Popular in Physics 2

This 10 page Class Notes was uploaded by Eleazar Batz on Wednesday September 30, 2015. The Class Notes belongs to PHYS 260 at Western Kentucky University taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/216684/phys-260-western-kentucky-university in Physics 2 at Western Kentucky University.

## Reviews for INTRO ELECTRICITY & MAGNETISM

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/30/15

Dr Barzilov s MWF Section Physics A Math Review Math Tools Q What do you get if you cross an apple with a coconut A Apple coconut sine theta Resultant Vector I Problem You wish to find the vector sum of vectors A and E Pictorially this is shown in the figure on the rig Mathematically you want to break the vector into x y and maybe 2 components and find the resultant vector Let A 62 7 9 And if 122 69 HAEHJlt612V 7 62 y 7 6 tan 9 7 612 System of Eguations I Let6x7y 15 I And 4X 3y 9 I Now find X and y which satisfy these equations Use method of minorsquot o M 9 39 Wantincn El System of Equations cont d The solution for x is found by creating a minor wherein the constants in the equation are substituted in place of the x value and the value of the minor is found It is then divided by the value of the determinant 15 7 9 3 Z 153 79 det 46 Then back substitute the value of x into my initial equation and solve for y x 2347 6 2347 7y 15 and solve for y y 1304 OR use the minors again 6 15 4 9 269 415 det 46 01304 Larger Systems Larger systems are broken down into their resultant minors Forexampe 6X7y102 12 9X15y2260 5x12y10215 6 7 10 15 2 9 2 9 15 det 9 15 2 6 7 10 2 3434 12 10 5 10 5 12 5 12 1 12 7 10 6015 2 15 12 10 X det Spherical Coordinates I Cartesian coordinates X y z Spherical coordinates r 6 Cylindrical Coordinates Eylindric 3 Coordinates Z Cartesian coordinates X y z Spherical coordinates r g z xrcos yrsin zz 1 rx2 yzE lx2 y2 tan 1l X Partial Derivatives I So what is the difference between quotd andB the variable X d like ddX means the function only contains When the function contains not just X but may be y and 2 we use the partial differential a For example fxyzxyz 31i Bx Bx xyz W Note that the variables y and z are held constant when the differential operator acts on the function What is the solution to 3m 7 a i 2 3y SK 0 Introduction to Del You can now make a special differential operator called del Del is defined as lt1 ll Treat del as a vector and thus you can apply the dot and cross products to them But first let s recall the dot and cross product The dot or Scalar Product The scalar product is A 1135 ay az2 defined as the multiplication of two and vectors in such a way l b 21 Ab 2 that result is a vector 1 yy z Then 3 E 1le ayby 1le I 0is the angle between A and B or 31 cos 6 Cross or Vector Product The vector product is the multiplication of two vectors such that the result is a vector and furthermore the resulting vector is perpendicular to the either of the two original vectors The best way to find a vector product is to set it up as a determinant as shown on the right 22 9 2 AX aX ay az bx by bz gtl x E aybz azby y c axbz lt1sz 9 axby aybx Xx 9 0 His the angle between A and B First application of del Gradient The gradient is defined as the shortest or steepest path up a mountain or down into a valley Let s go back to fgtltyz then Vf VW yzf xz xy2 You see that grad 1 makes a vector which points in a particular direction Also note that grad 1 takes a scalar function and makes a vector of it A particle which travels through a region of space wherein the potential energy Ugtltyz varies as a function of space has a force exerted on it equivalent to a 8U 8U 8U F VU 7 7 7 l 623 ayjyl azjz The Scalar Product and V I We can apply V to the scalar product ie o VA where A is some vector I VA is called the divergence of A or divAquot I Geometrically we are discussing if A is diverging from some central point A is diverging is m from a central dlvergmg from a central point potnt so so DivA is equal to DivA is equal some value to zero The Vector Product and V I We can apply V to the vector product ie o VxA where A is some vector I VXA is called the curl of A or curlA I Geometrically we are discussing if A is curling around some central 1 I A is curlin A Is not curling around a 9 around a central central point potnt so so curlA is curlA IS equal equal to some to zero value What about A V and A x V I These two products do not describe the geometrical properties I A V is not equal to V A due to the nature of the differential operator I A VU would be equivalent to A F where F is a force described by VU I Likewise for A x VU Two Special Integrals I Integrating over a closed loop d I Integrating over a closed surface B dEi Integrating over a closed loop The loop can be circular or rectangular O d rd6 lSEd Blt2zrrgt From 0 to 27 Looping from Point A to Point D B using straight line segments C d dsAfrdsB idscfrdsD i Closed Surface Integral The vector nhat is normal to the surface This means that da must consist of the differential distance in the phidirection multiplied by the differential distance in Theta is integrated from 0to 7 the theta direction so and phi is integrated from 0 to 27 do Rsin 6d Rd Th f if Ed d I PI 39 ere ore 9P9 5 on y on R2 sm 6 d6 W5 the E d5 E47z1 2

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.