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 Insidea 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 theprojection of somevector quantity is projected on a straight or curved linear path connecting two points, and theproduct of vector’s projection times infinitesimal path distanceis summed. Thesimplest lineintegral is just the sum over thepath 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 themagnetic 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 magnetic field,
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