PHYS 272 Matter and Interactions II Electric And

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ PHYSICS 272 Electric & Magnetic Interactions Lecture 10 Electric Potentials [EMI 17. 5 -17. 8] Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ For a conductor in equilibrium: The potential difference is zero between any two locations inside. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Potential Difference in Metal In static equilibrium What is E inside metal? E = 0 In static equilibrium the electric field is zero at all locations along any path through a metal. What is the potential difference (Vf – Vi)? f i The potential difference is zero between any two locations inside the metal, and the potential at any location must be the same as the potential at any other location. Is V zero everywhere inside a metal? No! But it is constant Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Example: metal inserted into capacitor In static equilibrium -Q 1 1 mm +Q 1 Insert a 1 mm thick metal slab into the center of the capacitor. Metal slab polarizes and has charges +Q 2 and -Q 2 on its surfaces. 2000 V/m What are the charges Q 1 and Q 2? E inside metal is zero Q 2=Q 1 Now we have 2 capacitors instead of one d =3 mm V inside metal slab is zero! There is no “conservation of potential”! V = 4 V Charges +Q 2 and –Q 2 Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Clicker Question 1 300 V/m A B 0. 02 m What is VB-VA? 0. 03 m A) B) C) D) E) 0. 04 m 270 V -18 V 6 V -6 V Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Clicker Question 1 300 V/m A B 0. 02 m What is VB-VA? 0. 04 m 0. 03 m A) B) C) D) E) 270 V -18 V 6 V -6 V D Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Clicker Question 2 Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Clicker Question 2 A Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Two adjacent regions with different fields C In general, From A to C, ∆V 1 = -E 1 x(x. C - x. A) From C to B, ∆V 2 = -E 2 x(x. B - x. C) From A to B, ∆V = ∆V 1 + ∆V 2 = Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Example: x Q > 0, ∆V < 0 If x. B → , VB → 0 Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Recall Physics I: The potential energy differences depend only on the initial and final states of a system and are independent of path. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Example: Different Paths near Point Charge 1. Along straight radial path: rf ri +q Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Example: Different Paths near Point Charge 2. Special case i. A: AB: BC: + Cf: Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Superposition Principle for Potential Qi 1. 2. 3. Cut the charge distribution into pieces Calculate the contribution to the potential due to each piece Use superposition to get the total potential We typically pick reference point of potential at infinity to be 0: Potential due to point charge Q (at origin) at any given point ( ) in space: Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Potential of a Uniformly Charged Ring Q Method 1: Divide into point charges and add up contributions due to each charge Superposition Principle for Electric Potential Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Potential of a Uniformly Charged Ring Q Method 2: Integrate electric field along a path Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Potential of a Uniformly Charged Ring Q What is V for z>>R ? The same as for a point charge! Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Potential Inside a Uniformly Charged Hollow Sphere =0 Outside (r>R), looks like point charge Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Potential Difference in an Insulator Electric field in capacitor filled with insulator: Enet=Eplates+Edipoles Eplates=const (in capacitor) Edipoles, A A 1 2 3 Edipoles, B Edipoles=f(x, y, z) B Travel from B to A: Edipoles is sometimes parallel to dl, and sometimes antiparallel to dl 4 5 Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Potential Difference in an Insulator Instead of traveling through inside – travel outside from B to A: A Edipoles, average B Effect of dielectric is to reduce the potential difference. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Dielectric Constant Electric field in capacitor filled with insulator: Enet=Eplates-Edipoles K – dielectric constant Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Dielectric Constant Inside an insulator: Dielectric constant for various insulators: vacuum air typical plastic Na. Cl water strontium titanate 1 (by definition) 1. 0006 5 6. 1 80 310 Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Potential Difference in Partially Filled Capacitor d +Q -Q K A s B x Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Electric Potential Energy of Two Particles Fint q 2 r 12 q 1 The potential energy of a pair of particles is defined as: Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 7