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NNSE508_EM-L2-magnetic_field

NNSE508_EM-L2-magnetic_field - 1 Lecture contents Magnetic...

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NNSE 508 EM Lecture #2 1 Lecture contents Magnetic field Ampere’s law Lorentz force, cyclotron frequency, Hall effect Dipole moment, circulation electron, spin
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NNSE 508 EM Lecture #2 2 Magnetostatics: Ampere’s Law of Force Ampere’s law of force is the “law of action” between current carrying circuits through magnetic field. Experimental facts: The magnitude of the force is inversely proportional to the distance squared. The magnitude of the force is proportional to the product of the currents carried by the two wires. The force acting on a current element I 2 d l 2 by a current element I 1 d l 1 is given by Experimental facts: Two parallel wires carrying current in the same direction attract. Two parallel wires carrying current in the opposite directions repel. A short current oriented perpendicular to another current experiences no force. I 1 I 2 F 12 F 21 I 1 I 2 F 12 F 21 12 2 2 1 1 0 12 2 12 4 R I l I l a F R Permeability of free space 0 = 4 10 -7 {F W /m} ={N/A 2 } unit vector in direction of I 2 from I 1 I 1 F 12 = 0 I 2
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NNSE 508 EM Lecture #2 3 Magnetic field The total force acting on a circuit C 2 having a current I 2 by a circuit C 1 having current I 1 is given by Similar to Coulomb’s law, magnetic field can be introduced An infinitely small current element Id l immersed in a region of magnetic flux density B , experiences a force d F 12 2 1 2 1 0 1 2 2 12 4 R C C dl dl a I I F R   12 2 1 1 1 0 2 2 2 12 4 R C C I dl a F I dl R   12 1 1 1 0 2 12 T 4 R C I dl a B R
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