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How Relativity Connects Electric and Magnetic Fields

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By Professor Michael Fowler, University of Virginia

A Magnetic Puzzle…

Suppose we have an infinitely long straight wire, having a charge density of electrons of –λ coulombs per meter, all moving at speed v to the right (recall typical speeds are centimeters per minute) and a neutralizing fixed background of positive charge, also of course λ coulombs per meter.  The current in the wire has magnitude I = λv (and actually is flowing to the left, since the moving electrons carry negative charge).

Suppose also that a positive charge q is outside the wire, a distance r from the axis, and this outside charge is moving at the same exact velocity as the electrons in the wire.

So how does this lead to the effect we know as magnetism? Read on . . .

ow Relativity Connects Electric and Magnetic Fields

AP Physics Learning Objectives

Essential Knowledge 1.D.3: Properties of space and time cannot always be treated as absolute.

a. Relativistic mass–energy equivalence is a reconceptualization of matter and energy as two manifestations of the same underlying entity, fully interconvertible, thereby rendering invalid the classically separate laws of conservation of mass and conservation of energy. Students will not be expected to know apparent mass or rest mass.

b. Measurements of length and time depend on speed. (Qualitative treatment only.) physics

Learning Objective 1.D.3.1: The student is able to articulate the reasons that classical mechanics must be replaced by special relativity to describe the experimental results and theoretical predictions that show that the properties of space and time are not absolute.
[Students will be expected to recognize situations in which non-relativistic classical physics breaks down and to explain how relativity addresses that breakdown, but students will not be expected to know in which of two reference frames a given series of events corresponds to a greater or lesser time interval, or a greater or lesser spatial distance; they will just need to know that observers in the two reference frames can “disagree” about some time and distance intervals.]

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