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 12 Magnetic Fields [EMI 18. 5 -18. 7] Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ The Magnetic Effects of Currents Conclusions: • The magnitude of B depends on the amount of current • A wire with no current produces no B • B is perpendicular to the direction of current • B under the wire is opposite to B over the wire Oersted effect: discovered in 1820 by H. Ch. Ørsted How does the field around a wire look like? Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ The Magnetic Effects of Currents The moving electrons in a wire create a magnetic field Principle of superposition: What can you say about the magnitudes of BEarth and Bwire? What if BEarth were much larger than Bwire? Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Exercise A current-carrying wire is oriented N-S and laid on top of a compass. The compass needle points 27 o west. What is the magnitude and direction of the magnetic field created by the wire Bwire if the magnetic field of Earth is BEarth= 2 10 -5 T (tesla). Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Electron current vs. conventional current Number of electrons? Electron current Number of electrons per second Conventional current Coulombs per second, or Amperes where n is the mobile electron density, A is the cross-sectional area of wire, is the average drift speed of electrons, and in a metal. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Typical Mobile Electron Drift Speed Typical electron current in a circuit is ~ 1018 electrons/s. What is the drift speed of an electron in a 1 mm thick copper wire of circular cross section? Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Conventional Current Metals: current consists of electrons Semiconductors: n-type – electrons p-type – positive holes In some materials current moving charges are positive: Ionic solution “Holes” in some materials (same charge as electron but +) Observing magnetic field around copper wire: Can we tell whether the current consists of electrons or positive ‘holes’? The prediction of the Biot-Savart law is exactly the same in either case. conventional current: Units: C/s A (Ampere) Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Why? See next page. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Formula for one moving charge Sum all the moving charges in the short segment of wire Total number of moving charges Recall Therefore Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Superposition Principle Magnetic Field for a extended curre y x Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

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 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Clicker Question 1 Current carrying wires below lie in X-Y plane. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Clicker Question 1 Current carrying wires below lie in X-Y plane. C Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Magnetic Field of Current Distributions Four-step approach: 1. Cut up the current distribution into pieces and draw B 2. Write an expression for B due to one piece 3. Add up the contributions of all the pieces 4. Check the result Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ 1. Draw ∆B for an arbitrary piece 2. Write an expression for ∆B (2. 1) Direction: Right-hand rule ∆B got cancelled out; only consider ∆Bz (2. 2) Magnitude: Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ 3. Add up all the pieces Direction of B-field is along the z-axis (right-hand rule for loops) Recall E-field of a ring Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ A Coil of Wire What if we had a coil of wire? single loop: For N turns: Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Magnetic dipole moment vs. Electric dipole moment Define a vector, , pointing in the direction of the B-field. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Magnetic Dipole Moment far from coil: magnetic dipole moment: far from dipole: - vector in the direction of B Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

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 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Clicker Question 2 C Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10

PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions http: //www. physics. purdue. edu/academic_programs/courses/phys 272/ Twisting of a Magnetic Dipole The magnetic dipole moment acts like a compass needle! In the presence of external magnetic field a current-carrying loop rotates to align the magnetic dipole moment along the field B. Fall 2010 Prof. Yong Chen (yongchen@purdue. edu) Prof. Michael Manfra (mmanfra@purdue. edu) Lecture 10