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Ampere’s Law PH 203 Professor Lee Carkner Lecture 17

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Test 2 on Monday Covers everything since last test through Wednesday 10 multiple choice (20 points) 4 problems (20 points each) Equations and constants given but not labeled Bring calculator No PDA’s, no cellphones, no sharing Study PAL’s Notes Homework

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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 integral of the product of ds and B around the entire path is equal to 0 i Where 0 = 4 X 10 -7 T m /A and is called the permeability of free space ∫ B ds = 0 i where i is the charge enclosed by the path

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B Field for a Wire ∫ B ds = 0 i or B ∫ ds = 0 i Since B is the same everywhere around the circle B 2 r = 0 i B = 0 i/2 r Magnetic field a distance r from a long straight wire with current i

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B Field within a Wire e.g. within the wire In this case the B field is still B = 0 i enc /2 r If the total radius of the wire is R i enc = i( r 2 / R 2 ) B = ( 0 ir)/(2 R 2 )

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Force on Two Parallel Wires The B field then will exert a force on the other wire B = 0 i/2 d F = BiL = 0 iiL/2 d F = ( 0 i 1 i 2 L)/(2 d)

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Next Time Read 29.5-29.6 Problems: Ch 29, P: 9, 28, 37, 42, 49

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Consider a charged particle in a circular orbit in a magnetic field. If the charge on the particle is doubled, and the velocity of the particle is doubled, what happens to the radius of the orbit? A)¼ the original B)½ the original C)the radius stays the same D)2 times the original E)4 times the original

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The force on a current-carrying wire in a magnetic field is strongest when, A)the current is parallel to the field lines B)the current is at a 30 degree angle to the field lines C)the current is at a 45 degree angle to the field lines D)the current is at a 60 degree angle to the field lines E)the current is perpendicular to the field lines

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Consider a vector that stands straight out from the face of a loop of wire that carries a current. The magnetic torque on the loop will be greatest when, A)the vector is aligned with the magnetic field B)the vector is at a 30 degree angle to the magnetic field C)the vector is at a 45 degree angle to the magnetic field D)the vector is at a 60 degree angle to the magnetic field E)the vector is perpendicular to the magnetic field

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