W02d1 electric dipoles and continuous charge distributions
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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

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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 distributions

Continuous Charge Distributions


Continuous charge distributions1

Continuous Charge Distributions

Break distribution into parts:

V

E field at P due to Dq

Superposition:


Continuous sources charge density

Continuous Sources: Charge Density


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?


Examples of continuous sources finite line of charge

Examples of Continuous Sources: Finite Line of Charge

E field on perpendicular bisector


Examples of continuous sources finite line of charge1

Examples of Continuous Sources: Finite Line of Charge

E field off axis


Examples of continuous sources finite line of charge2

Examples of Continuous Sources: Finite Line of Charge

Grass seeds of total E field


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

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

1) Think about it

Symmetry!

2) Define Variables


Ring of charge1

Ring of Charge

3) Write Equation


Ring of charge2

Ring of Charge

4) Integrate

This particular problem is a very special case because

everything except dq is constant, and


Ring of charge3

Ring of Charge

5) Clean Up

6) Check Limit


Group problem uniformly charged disk

Group Problem: Uniformly Charged Disk

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

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

  • 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


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