Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions PHYSICS 272 Electric & Magnetic Interactions Lecture 3 Superposition of electric field; Dipoles Note: for iclickers to work: 1) must be turned on prior to answering question, 2) set proper frequency “AB” – hold down power button for ~2 sec, then press “A” and “B”

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions The net electric field at a location in space is a vector sum of the individual electric fields contributed by all charged particles located elsewhere. The Superposition Principle The electric field contributed by a charged particle is unaffected by the presence of other charged particles.

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions The Superposition Principle

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions The E of a Uniformly Charged Sphere Can calculate using principle of superposition: for r>R (outside) for r<R (inside)

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Electric dipole: Two equally but oppositely charged point-like objects What is the E field far from the dipole (r>s)? +q-q s Example of electric dipole: HCl molecule The Superposition Principle The electric field of a dipole:

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions +q-q s x y z Choice of origin: use symmetry Calculating Electric Field Choice of the origin

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 1. E along the x-axis

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions if r>>s, then While the electric field of a point charge is proportional to 1/r 2, the electric field created by several charges may have a different distance dependence. Approximation: Far from the Dipole

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 2. E along the y-axis

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 2. E along the y-axis if r>>s, thenat

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 3. E along the z-axis Due to the symmetry E along the z-axis must be the same as E along the y-axis! at or at

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Other Locations

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions The Electric Field + - Point Charge: Dipole: for r>>s : at +q -q s x y z at

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Example Problem A dipole is located at the origin, and is composed of particles with charges e and –e, separated by a distance 2  m along the x- axis. Calculate the magnitude of the E field at m. y 2Å2Å 200Å E=? Since r>>s: Using exact solution: x

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions What is the direction of the electric field at location X, due to the dipole? Question 1 (Chap. 14) A C B E D - + X

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Question 2 (Chap. 14) Locations 1 and 2 are equidistant from the center of the dipole. At which location is the magnitude of the electric field larger? A. at location 1 B. at location 2 C. magnitudes are the same d d -

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Interaction of a Point Charge and a Dipole Direction makes sense? - negative end of dipole is closer, so its net contribution is larger What is the force exerted on the dipole by the point charge? - Newton’s third law: equal but opposite sign

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Dipole Moment x: y, z: Dipole moment: p = qs, direction from –q to +q r>>s Dipole moment is a vector pointing from negative to positive charge The electric field of a dipole is proportional to the

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Dipole in a Uniform Field Forces on +q and –q have the same magnitude but opposite direction It would experience a torque about its center of mass. What is the equilibrium position? Electric dipole can be used to measure the direction of electric field.

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Choice of System Multiparticle systems: Split into objects to include into system and objects to be considered as external. To use field concept instead of Coulomb’s law we split the Universe into two parts: the charges that are the sources of the field the charge that is affected by that field Example: Oscilloscope Charges on metal plates are the sources of an uniform E field

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Convenience: know E at some location – know the electric force on any charge: Example: if E>3  10 6 N/C air becomes conductor Limitations to Coulomb’s law Nothing can move faster than light c c = 300,000 km/s = 30 cm/ns Can describe the electric properties of matter in terms of electric field – independent of how this field was produced. Coulomb’s law is not completely correct – it does not contain time t nor speed of light c. v<<c !!! A Fundamental Rationale

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Chapter 15 Matter and Electric Fields

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Matter is made out of atoms. Atom contains charged particles: electrons (-e), protons (+e) Neutral atom: number of electrons and protons is equal: Example: Hydrogen atom: 1 proton, 1 electron net charge = (+e) + (-e)=0 Sodium atom: 11 protons, 11 electrons Sodium atom (Na) can lose an electron: Sodium ion (Na + ): (+11e) + (-10e) = +e Ordinary matter is electrically neutral. However, can be charged by adding/removing charged particles Net Charge

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 2 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions The net charge of a system and its surroundings cannot change If one object gets charged positively, there must be an object which gets charged negatively. Conservation of Charge The net electric charge is conserved in any physical process. Charge can be transferred from one object to another.