Magnetism (part 5)

Magnetism (part 5) - The Magnetic Field of a Current F = qE...

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Magnetism The Magnetic Field of a Current x x x x x x x x x x x x x x x x x x v F B q → → → → → → → → → → v F B q × ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ v F = 0 B q B v q E q F × + =
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Physics 113 Dr. Renat Letfullin 2 Line Integrals Another form of Ampere’s Law 1. Example : The Magnetic Field Inside a Current-Carrying Wire Magnetic Field of Solenoids Motion of Charge in an Uniform magnetic filed The Earth’s Van Allen Belt The Hall Effect Today. . .
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Physics 113 Dr. Renat Letfullin 3 Clicker Question 1 What is the current direction in the loop and which side is the north magnetic pole? (a) Current cw, N pole on top; (b) Current cw, N pole on bottom; (c) Current ccw, N pole on top; (d) Current ccw, N pole on bottom;
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Physics 113 Dr. Renat Letfullin 4 Line Integrals (1) A line integral is a special kind of vector integral in which the projection of some vector quantity is projected on a straight or curved linear path connecting two points, and the product of vector’s projection times infinitesimal path distance is summed. The simplest line integral is just the sum over the path length L : f k k i L s ds = We have previously seen this kind of integration in our discussion of work: f f s i i W F ds F ds = =
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Physics 113 Dr. Renat Letfullin 5 Line Integrals (2) Now consider a line integral in the presence of a magnetic field. Divide the path up into line segments of length s . At the k th segment the magnetic field is B k . f k k k i B s B ds ⋅∆ f f f i i i B ds Bds B ds BL = = = If B is always in the same direction as ds and constant over the path, then:
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Physics 113 Dr. Renat Letfullin 6 Line Integrals Made Easy If B is everywhere perpendicular to the path of integration ds , then: 0 f i B ds = If B is everywhere parallel to the path of integration ds , then: f i B ds BL =
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Physics 113 Dr. Renat Letfullin 7 Ampere’s Law A special case of a line integral is one that runs in a closed path and returns to where it started, i.e., a line integral around a closed curve, which, for a
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Magnetism (part 5) - The Magnetic Field of a Current F = qE...

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