# W02D1 Electric Dipoles and Continuous Charge Distributions - PowerPoint PPT Presentation

1 / 31

W02D1 Electric Dipoles and Continuous Charge Distributions. Math Review Tuesday Tues Feb 14 from 9-11 pm in 32-082 PS 1 due Tuesday Tues Feb 14 at 9 pm in boxes outside 32-082 or 26-152 W02D2 Reading Assignment Course Notes: Chapter Course Notes: Sections 4.1-4.2, 4.7

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

W02D1 Electric Dipoles and Continuous Charge Distributions

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

### W02D1Electric Dipoles and Continuous Charge Distributions

Math Review Tuesday Tues Feb 14 from 9-11 pm in 32-082

PS 1 due Tuesday Tues Feb 14 at 9 pm in boxes outside 32-082 or 26-152

W02D2 Reading Assignment Course Notes: Chapter Course Notes: Sections 4.1-4.2, 4.7

Make sure your clicker is registered

## Announcements

### Outline

Electric Dipoles

Force and Torque on Dipole

Continuous Charge Distributions

### Nature Likes to Make Dipoles

http://youtu.be/EMj10YIjkaY

## Demonstration: Dipole in a Van de Graaff Generator D22

E

### Concept Question: Dipole in Non-Uniform Field

A dipole sits in a non-uniform electric field E

Due to the electric field this dipole will feel:

• force but no torque

• no force but a torque

• both a force and a torque

• neither a force nor a torque

E

### Concept Question Answer: Non-Uniform Field

Answer: 3. both force and torque

Because the field is non-uniform, the forces on the two equal but opposite point charges do not cancel.

As always, the dipole wants to rotate to align with the field – there is a torque on the dipole as well

## Continuous Charge Distributions

### Continuous Charge Distributions

Break distribution into parts:

V

E field at P due to Dq

Superposition:

### Group Problem: Charge Densities

• A solid cylinder, of length L and radius R, is uniformly charged with total charge Q.

• What is the volume charge density ρ?

• What is the linear charge density λ?

• What is the relationship between these two densities ρ and λ?

### Examples of Continuous Sources: Finite Line of Charge

E field on perpendicular bisector

E field off axis

### Examples of Continuous Sources: Finite Line of Charge

Grass seeds of total E field

A rod of length L lies along the x-axis with its left end at the origin. The rod has a uniform charge density λ. Which of the following expressions best describes the electric field at the point P

## Concept Question Electric Field of a Rod

A rod of length L lies along the x-axis with its left end at the origin. The rod has a uniform charge density λ. Which of the following expressions best describes the electric field at the point P

## Concept Question Electric Field of a Rod: Answer

### Group Problem: Line of Charge

Point P lies on perpendicular bisector of uniformly charged line of length L, a distance s away. The charge on the line is Q. Find an integral expression for the direction and magnitude of the electric field at P.

### Hint on Line of Charge Group Problem

Typically give the integration variable (x’) a “primed” variable name. ALSO: Difficult integral (trig. sub.)

### E Field from Line of Charge

Limits: s >> L (far away) and s << L (close)

Looks like the E field of a point charge if we are far away

Looks like E field of an infinite charged line if we are close

### Examples of Continuous Sources: Ring of Charge

E field on the axis of the ring of charge

### Examples of Continuous Sources: Ring of Charge

E field off axis and grass seeds plot

A uniformly charged ring of radius a has total charge Q. Which of the following expressions best describes the electric field at the point P located at the center of the ring?

## Concept Question Electric Field of a Ring

A uniformly charged ring of radius a has total charge Q. Which of the following expressions best describes the electric field at the point P located at the center of the ring?

## Concept Question Electric Field of a Ring: Answer

### Demonstration Problem: Ring of Charge

Aring of radius a is uniformly charged with total charge Q. Find the direction and magnitude of the electric field at the point P lying a distance x from the center of the ring along the axis of symmetry of the ring.

### Ring of Charge

Symmetry!

2) Define Variables

### Ring of Charge

3) Write Equation

### Ring of Charge

4) Integrate

This particular problem is a very special case because

everything except dq is constant, and

5) Clean Up

6) Check Limit

### Group Problem: Uniformly Charged Disk

P on axis of disk of charge, x from center

Find E at P

### Disk: Two Important Limits

Limits: x >> R (far) and x << R (close)

Looks like E of a point charge far away

Looks like E field of an infinite charged plane close up

### Scaling: E for Plane is Constant

• Dipole: E falls off like 1/r3

• Point charge:E falls off like 1/r2

• Line of charge:E falls off like 1/r

• Plane of charge: E constant