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Ampere’s Law Physics 102 Professor Lee Carkner Lecture 19

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PAL #18 Magnetic Force How long would it take an electron to complete one circular orbit around a 1 G magnetic field? Distance around circle is circumference: Can find velocity from equation: v = rqB/m t = (2 r)/(rqB/m) = t = [(2)( )(9.1X10 -31 )]/[(1.6X10 -19 )(1X10 -4 )] t =

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Currents and Magnetism It is also true that moving charged particles produce magnetic fields Serious magnetic fields are produced by currents What is the magnitude and direction of these fields?

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Magnetic Field from a Current in a Wire Needle deflected tangentially to the wire cross section How can we find the direction and magnitude of the B field for any situation?

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Right Hand Rule Revisited Grasp the wire with your thumb in the direction of the current and your curled fingers indicate the direction of the field

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Ampere’s Law To find the magnitude of the B field we use Ampere’s law The sum of the product of L and B around the entire path is equal to 0 I We can express Ampere’s law as: B L = 0 I

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B Field for a Wire Use Ampere’s law for a circle of radius r around the wire Since B is the same everywhere around the circle B 2 r = 0 I Magnetic field a distance r from a long straight wire with current I

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Today’s PAL Consider two parallel metal rails 1 cm apart and each carrying 100000 A of current in opposite directions What is the direction and magnitude of B at a point halfway in-between them? What is the direction and magnitude of the force on a conductor also carrying 100000 A that connects the two rails? I I

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Force on Two Parallel Wires The B field then will exert a force on the other wire F = BIL = 0 IIL/2 d F = 0 I 1 I 2 L/2 d

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Magnetic Field: Loop Can apply the right hand rule all the way around Loop acts as a bar magnet

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Magnetic Field: Solenoid What happens if you stack several loops up? You produce a solenoid Field inside the solenoid is strong and uniform (far from the ends)

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Electromagnet We can write an expression for the solenoid magnetic field: B = 0 nI If you put a piece of iron in the center you get an electromagnet

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Next Time Exam #2 Same format as Exam #1 Covers chapters 16-20 Practice problems posted on WebAssign Will not count for grade Reading and homework for Monday on webpage

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