DOC PREVIEW
MIT 8 02T - Electric Dipoles and Continuous Charge Distributions

This preview shows page 1-2-3-21-22-23-42-43-44 out of 44 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 44 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

1 W02D1 Electric Dipoles and Continuous Charge DistributionsOnline Registration If you are in a M/W/F class for 8.02, you will need to register for the course “8.02r-MW Electricity and Magnetism (Monday and Wednesday)”. If you are in a Tuesday/Thursday/Friday class for 8.02, register for “8.02r-TTh: Electricity and Magnetism (Tuesday and Thursday)”. The following link will get you to either course and the web site will require certificates: https://lms.mitx.mit.edu/Announcements Math Review Week Two Tues from 9-11 pm in 26-152 PS 1 Handwritten due Week Two Tuesday at 9 pm in boxes outside 32-082 or 26-152 PS 1 Online due Week Two Wednesday at 8:30 am Finalize Group Formations Make sure your clicker is registered 34 Outline Review: Electric Field Main Problem of Electrostatics: Electric Field Lines Electric Dipoles Force and Torque on Dipole Continuous Charge Distributions5 Review: Electric Field due to Source Charges The electric field at a point P due to a charged object (source) with charge qs is the force acting on a test point-like charged object with charge qt at that point P, divided by the charge qt : Es(P) ≡Fst(P)qt Es(P) = keqsrst2ˆrs(P)Units: N/C6 Types of Source Charges Positively charged point-like object Negatively charged point-like object Discrete number of charged point-like objects Example: Electric Dipole Continuous Distribution of charged objects Examples: Charged wire Charged disc Charged sphere Very large charged plane7 Concept Question: Electric Field Two charged objects are placed on a line as shown below. The magnitude of the negative charge on the right is greater than the magnitude of the positive charge on the left, . Other than at infinity, where is the electric field zero? 1. Between the two charged objects. 2. To the right of the charged object on the right. 3. To the left of the charged object on the left. 4. The electric field is nowhere zero. 5. Not enough info – need to know which is positive. qR> qL8 Force on Charged Object in Electric Field due to Source Charges Force on a charged object with charge q at a point P in an electric field due to a source is: Es Fq(P) = mqaq(P)qEs(P) = mqaq(P)9 Newton’s Second Law Force on a charged object with charge q at a point P in an electric field due to a source is: Fq(P) = mqaq(P)qEs(P) = mqaq(P) Es10 Electric Field Lines 1. Direction of field at any point is tangent to field line at that point 2. Field lines point away from positive charges and terminate on negative charges 3. Field lines never cross each other11 Concept Question: Field Lines Electric field lines show: 1. Directions of forces that exist in space at all times. 2. Directions in which positive charges on those lines will accelerate. 3. Paths that charges will follow. 4. More than one of the above. 5. I don’t know.12 Electric Dipole13 Nature Likes to Make Dipoles http://youtu.be/EMj10YIjkaY !14 Demonstration: Electric field Lines D1615 Electric Dipole Two equal but opposite charges +q and –q, separated by a distance 2a p ≡ q2aˆj = 2qaˆjpoints from negative to positive charge prq -q 2a Dipole moment two charges prDipole moment for neutral charge distribution, N point charges p ≡ qii=1i= N∑ri16 Electric Field Created by Dipole Week 01 Friday Problem Solving Ex= keqΔxr+3−Δxr−3⎛⎝⎜⎞⎠⎟= keqxx2+ ( y − a)2⎡⎣⎤⎦3/2−xx2+ ( y + a)2⎡⎣⎤⎦3/2⎛⎝⎜⎜⎞⎠⎟⎟ Ey= keqΔy+r+3−Δy−r−3⎛⎝⎜⎞⎠⎟= keqy − ax2+ ( y − a)2⎡⎣⎤⎦3/2−y + ax2+ ( y + a)2⎡⎣⎤⎦3/2⎛⎝⎜⎜⎞⎠⎟⎟ ˆrr2=rr3=Δxr3ˆi +Δyr3ˆj17 Point Dipole Approximation r >> a Ex(r,θ) →3p4πε0r3sinθcosθ Ey(r,θ) →p4πε0r33cos2θ− 1( )Finite Dipole Point Dipole You can show… For distances18 Concept Question: Dipole Field As you move to large distances r away from a dipole, the electric field will fall-off as: 1. 1/r2, just like a point charge 2. More rapidly than 1/r2 3. More slowly than 1/r219 Demonstration: Dipole in a Van de Graaff Generator D2220 Dipole in Uniform Field E = Eˆi p = 2qa(cosθˆi + sinθˆj) Fnet=F++F−= qE + (−q)E = 0Total Net Force: Torque on Dipole: tends to align with the electric field p τ =r ×F = (2a)(qE)sin(θ) =p ×E τ= rF+sin(θ) = pE sin(θ)Charges fixed at ends of rod21 Torque on Dipole Total Field (dipole + background) shows torque: • Field lines transmit tension • Connection between dipole field and constant field “pulls” dipole into alignment22 Concept Question: Dipole in Non-Uniform Field A dipole sits in a non-uniform electric field E E Due to the electric field this dipole will feel: 1. force but no torque 2. no force but a torque 3. both a force and a torque 4. neither a force nor a torque23 Continuous Charge Distributions24 ( )?P =ErV Continuous Charge Distributions Q = Δqii∑Break distribution into parts: ΔE = keΔqr2ˆrE field at P due to Superposition: E = ΔE∑→ dE∫ → dqV∫∫∫ → dE = kedqr2ˆr Δq25 Continuous Sources: Charge Density Length L=LwL Area = A = wLRLdLdQλ=dAdQσ=dVdQρ= ρ= Q / V (uniform) Volume = V =πR2L σ= Q / A (uniform) λ= Q / L (uniform)26 Group Problem: Charge Densities A solid cylinder, of length L and radius R, is uniformly charged with total charge Q. (a) What is the volume charge density ρ? (b) What is the linear charge density λ? (c) What is the relationship between these two densities ρ and λ?27 Examples of Continuous Sources: Finite Line of Charge LQ=λLength L=LdLdQλ=E field on perpendicular bisector28 Examples of Continuous Sources: Finite Line of Charge LQ=λLength L=LdLdQλ=E field off axis29 Examples of Continuous Sources: Finite Line of Charge LQ=λLength L=LdLdQλ=Grass seeds of total E field30 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 1.E(P) = −keλd′x(′x + d )3′x =0′x = L∫ˆi 2.E(P) = keλd′x(′x + d )3′x =0′x = L∫ˆi 3.E(P) = −keλd′x(′x + d )2′x =0′x = L∫ˆi 4.E(P) = keλd′x(′x + d )2′x


View Full Document

MIT 8 02T - Electric Dipoles and Continuous Charge Distributions

Documents in this Course
Load more
Download Electric Dipoles and Continuous Charge Distributions
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Electric Dipoles and Continuous Charge Distributions and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Electric Dipoles and Continuous Charge Distributions 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?