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EMLecture10

# EMLecture10 - Lecture 10 Notes 95.657 Electromagnetic...

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Lecture 10 Notes, 95.657 Electromagnetic Theory I, Fall 2011 Dr. Christopher S. Baird, UMass Lowell 1. Magnetostatics Introduction - All of the proceeding concepts have been applied to electrostatics: when static electric charges create static electric fields. - We now turn to a special case of electrodynamics known as magnetostatics: when electric charges move, but move in such a way that they create static magnetic fields. - The current density J is a vector field that describes the flow of charge at every point in space. - The current density is measured as the amount of positive charge per unit area per unit time, with the direction of the vector indicating the direction of charge flow. - When the electric current is confined in a wire, it is useful to integrate the current density over the cross-sectional area of the wire and find the total current I , or total electric charge flowing through the wire per unit time. - If the total charge Q V inside a volume V decreases, this means that some charge is flowing out passed the surface S bounding the volume. Charge is always conserved, it can be neither created nor destroyed: Q V t = S J n da - Use of the divergence theorem leads to the form: Q V t = V ∇⋅ J d x - Expand the total charge: t V d x = V ∇⋅ J d x - Shrink the volume down so that the integrands must be equal everywhere: ∂ρ t =∇⋅ J - This is the continuity equation in differential form. - Magnetostatics is the special case where we assume no build up or depletion of charge at any point: ∇⋅ J = 0 Definition of Magnetostatics (constant flow of charge) - The magnetic induction field B (also known as the magnetic flux density) is a vector field created by electrical currents. Magnetic fields directly produce forces on magnets (or other currents).

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2. The Biot-Savart Law - Using small straight wires containing currents and compass magnets, Oersted, Biot, and Savart experimentally found the following properties: - The magnetic field is directly proportional to the length dl of the small wire. - The magnetic field is directly proportional to the electrical current I in the wire. - The magnetic field is inversely proportional to the square of the distance r from the wire. - The magnetic field points in the direction normal to the plane in which the wire and observation point lie.
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EMLecture10 - Lecture 10 Notes 95.657 Electromagnetic...

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