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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

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W02d1 electric dipoles and continuous charge distributions
W02D1Electric Dipoles and Continuous Charge Distributions


Announcements

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

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Announcements


Outline
Outline

Electric Dipoles

Force and Torque on Dipole

Continuous Charge Distributions


Nature likes to make dipoles
Nature Likes to Make Dipoles

http://youtu.be/EMj10YIjkaY


Demonstration dipole in a van de graaff generator d22

Demonstration: Dipole in a Van de Graaff Generator D22


Concept question dipole in non uniform field

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


Concept question answer non uniform field

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 distributions1
Continuous Charge Distributions

Break distribution into parts:

V

E field at P due to Dq

Superposition:



Group problem charge densities
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?





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


Concept question electric field of a rod answer

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
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
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
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
Examples of Continuous Sources: Ring of Charge

E field on the axis of the ring of charge


Examples of continuous sources ring of charge1
Examples of Continuous Sources: Ring of Charge

E field off axis and grass seeds plot


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


Concept question electric field of a ring answer

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
Demonstration Problem: Ring of Charge Which of the following expressions best describes the electric field at the point

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
Ring of Charge Which of the following expressions best describes the electric field at the point

1) Think about it

Symmetry!

2) Define Variables


Ring of charge1
Ring of Charge Which of the following expressions best describes the electric field at the point

3) Write Equation


Ring of charge2
Ring of Charge Which of the following expressions best describes the electric field at the point

4) Integrate

This particular problem is a very special case because

everything except dq is constant, and


Ring of charge3
Ring of Charge Which of the following expressions best describes the electric field at the point

5) Clean Up

6) Check Limit


Group problem uniformly charged disk
Group Problem: Uniformly Charged Disk Which of the following expressions best describes the electric field at the point

P on axis of disk of charge, x from center

Radius R, charge density s.

Find E at P


Disk two important limits
Disk: Two Important Limits Which of the following expressions best describes the electric field at the point

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
Scaling: E for Plane is Constant Which of the following expressions best describes the electric field at the point

  • 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