Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions PHYSICS 272 Electric & Magnetic Interactions Lecture 11 Electric Potentials; Magnetic Fields [EMI ] Note: No Labs this week!

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Method 1: Divide into point charges and add up contributions due to each charge QQ Potential of a Uniformly Charged Ring Superposition Principle for Electric Potential

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Method 2: Integrate electric field along a path QQ Potential of a Uniformly Charged Ring

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions QQ What is V for z>>R ? The same as for a point charge! Potential of a Uniformly Charged Ring

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions =0 Potential Inside a Uniformly Charged Hollow Sphere Outside (r>R), looks like point charge

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Electric field in capacitor filled with insulator: E net =E plates +E dipoles E plates =const (in capacitor) E dipoles,A AB E dipoles,B E dipoles =f(x,y,z) Travel from B to A: E dipoles is sometimes parallel to dl, and sometimes antiparallel to dl Potential Difference in an Insulator

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Instead of traveling through inside – travel outside from B to A: BA E dipoles, average Potential Difference in an Insulator Effect of dielectric is to reduce the potential difference.

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Electric field in capacitor filled with insulator: E net =E plates -E dipoles K – dielectric constant Dielectric Constant

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Dielectric constant for various insulators: vacuum1 (by definition) air typical plastic5 NaCl6.1 water80 strontium titanate310 Inside an insulator: Dielectric Constant

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions +Q -Q s d K Potential Difference in Partially Filled Capacitor BA x

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Clicker Question 1

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Clicker Question 1 C)

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Clicker Question 2

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions B) Clicker Question 2

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions q1q1 q2q2 r 12 The potential energy of a pair of particles is defined as: Electric Potential Energy of Two Particles F int

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions q1q1 q6q6 q5q5 q4q4 q3q3 q2q2 Each (i,j) pair interacts: potential energy U ij Multiple Electric Charges

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Another view point: Energy is stored in electric fields (for small s) E volume Field energy density:(J/m 3 ) Energy expended by us was converted into energy stored in the electric field Energy Density of Electric Field No “self-force” on plate due to its own charge!

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Energy Density of Electric Field In the previous slide, the “system” is the set of two plates. Work, W external > 0, is done on the system by you – part of the “surroundings.” If the force exerted by you just offsets the attractive force, F by-plates, so that the plate moves with no gain in KE,

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions The energy density in a capacitor is 10 J/m 3. What is the magnitude of E inside the capacitor? Exercise What is the largest energy density achievable in a air-filled capacitor? E=3  10 6 V/m

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions In a multiparticle system we can either consider a change in potential energy or a change in field energy (but not both); the quantities are equal. The idea of energy stored in fields is a general one: Magnetic and gravitational fields can also carry energy. The concept of energy stored in the field is very useful: - electromagnetic waves Potential Energy and Field Energy

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions What is the change in electric potential energy associated with moving an electron from 1Å to 2Å from a proton? If an electron moves through a potential difference of 1 V there is a change in electric potential energy of 1 eV. 1 eV = e. (1 V) = ( C)(1 V) = 1.6  J Electron-Volt (eV) – Unit of Energy

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Chapter 18 Magnetic Field

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 7 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Biot-Savart law: Single moving charge Moving charged particles make a magnetic field