Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions PHYSICS 272 Electric & Magnetic Interactions Lecture 12 Magnetic Fields [EMI ]

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 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? The Magnetic Effects of Currents

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Principle of superposition: What can you say about the magnitudes of B Earth and B wire ? What if B Earth were much larger than B wire ? The Magnetic Effects of Currents The moving electrons in a wire create a magnetic field

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 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 B wire if the magnetic field of Earth is B Earth = 2   T (tesla). Exercise

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Electron current vs. conventional current 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. Number of electrons? Number of electrons per secondCoulombs per second, or Amperes Electron current Conventional current

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Typical electron current in a circuit is ~ electrons/s. What is the drift speed of an electron in a 1 mm thick copper wire of circular cross section? Typical Mobile Electron Drift Speed

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Metals: current consists of electrons Semiconductors: n-type – electrons p-type – positive holes conventional current: Conventional Current Units: C/s  A (Ampere) 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.

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Why? See next page.

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Formula for one moving charge Sum all the moving charges in the short segment of wire Total number of moving charges RecallTherefore

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions x y Superposition Principle  Magnetic Field for a extended current (straight wire)

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Clicker Question 1 Current carrying wires below lie in X-Y plane.

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Clicker Question 1 Current carrying wires below lie in X-Y plane. C

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 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 Magnetic Field of Current Distributions

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 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 ∆B z (2.2) Magnitude:

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 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 Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions What if we had a coil of wire? For N turns: single loop: A Coil of Wire

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Magnetic dipole moment vs. Electric dipole moment Define a vector,, pointing in the direction of the B-field.

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions far from coil:far from dipole: magnetic dipole moment:  - vector in the direction of B Magnetic Dipole Moment

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Clicker Question 2

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions Clicker Question 2 C

Fall 2010 Prof. Yong Chen Prof. Michael Manfra Lecture 10 Slide PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions 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. Twisting of a Magnetic Dipole