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Andres La Rosa Portland State University Lecture Notes PH-212 Magnetic field produced by a moving point charge Magnetic field at point P, Z P q Y q electrical charge (Coulomb) velocity (m/s) vector position (m) It aims from the charge q to the point P where we want to evaluate the magnetic field Magnetic field The unit is Tesla (T) P Z S q Y L Exercise Draw the vector MAGNETIC FIELD at the different points P, S, and L, respectively. Magnetic field produced by a current P Strategy: Divide the wire into small sections of length Δl P But notice, Example: Magnetic field produce by a current that flows along a straight wire Z P 0 We want to evaluate the magnetic field at a point "P' located at a distance "R" from the wire I Z I Δz P Contribution to the MAGNETIC FIELD at P from just one current segment Δ z Δz Δz For the case of an infinitely long wire: Q I P Infinitely long wire: Lateral View BP = BQ I Lateral View P Magnetic field line I Question: Question: What is the contribution to the magnetic field at P from the finite wire segment AB of length L ? T L/2 P L/2 I A Z Y X Question: What is the magnetic field at the point P caused by the segment AB that carries a current I ? T b L I P 0 a A Z X Y Exercise: Calculate the magnetic field at the points "G", "H", and "K" produced by the 2-meter wire that carries a current I = 0.5 Amps. T G H L=2m A K Z X Y Force between two parallel currents . . . . I1 . . . . . B. . . . I. . . 2 I1 - The magnetic field B1 produced by the current I1 at the site 2 is, B1 Magnetic field affecting the current I2 - A segment L of wire-2 is wire-2 immersed in a magnetic field B1 . So the wire will experience a force, Y Y 1 X We are assuming the wires are infinitely long ? The magnetic dipole moment The torque τ makes the dipole μ to have a tendency to be aligned along the external magnetic field. Magnetic potential energy of a dipole immersed in an external magnetic field As usual, the potential energy of the dipole will be given with respect to a configuration reference How much external work is needed to take the loop from the configuration-1 to the configuration-2? Example μ = NiA = 20 (0.1 Amp) (10-1m ) ( 5x10-2m ) Y = - 10-2 A-m2 X B = 0.5 T Z = = = Definition of the unit current: The Ampere Example . . . . . . . . x x x x x x x Amp 3030 Amp . . . . . . . . . . . . . . . . C B A 20 Amp D x x x x x x x B Calculate the net force acting on the loop that carries a 20 Amp currrent Along the segment BC the magnetic field produced by the 30 Amp wire is constant. Also, along the segment DA the magnetic field produced by the 30 Amp wire is constant. For these two cases, it is convenient to use the expression, Along the segment AB the magnetic field produced by the 30 Amp wire varies with position. Hence, in order to calculate te force on that segment of the loop, it is better to use, B A A X Z X Example M Y K P X L KL is a semi-circle of radius "R" What is the magnetic field at point "P"? Solution Contribution to the magnetic field at P from the section (- to K)? Contribution to the magnetic field at P from the section (L to )? Contribution to the magnetic field at P from the semicircle KL? 90 degrees. Inside the plane of the figure. Magnitude of the magnetic field at point P Exercise: Sketch the magnetic field of a circular coil of radius R carrying a current I. .. Z . . . . x x .B . . .. . .. x x x x B x x x x x xx .. Z X Z B B Y X Y Notation: = # of turns per unit length Question: In the figure above, where is the magnitude of the magnetic field higher, at point P or at point Q?