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## Ampere’s Law

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**Ampere’s Law**PH 203 Professor Lee Carkner Lecture 17**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**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?**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?**Grasp the wire with your thumb in the direction of the**current and your curled fingers indicate the direction of the field Right Hand Rule Revisited**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 m0i • Where m0 = 4p X 10-7 T m /A and is called the permeability of free space ∫ B ds = m0i • where i is the charge enclosed by the path**B Field for a Wire**∫ B ds = m0i or B ∫ ds = m0i • Since B is the same everywhere around the circle B 2pr = m0i B = m0i/2pr • Magnetic field a distance r from a long straight wire with current i**B Field within a Wire**• e.g. within the wire • In this case the B field is still B = m0ienc/2pr • If the total radius of the wire is R ienc = i(pr2/pR2) B = (m0ir)/(2pR2)**Force on Two Parallel Wires**• The B field then will exert a force on the other wire B = m0i/2pd F = BiL = m0iiL/2pd F = (m0i1i2L)/(2pd)**Next Time**• Read 29.5-29.6 • Problems: Ch 29, P: 9, 28, 37, 42, 49**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? ¼ the original ½ the original the radius stays the same 2 times the original 4 times the original**The force on a current-carrying wire in a magnetic field is**strongest when, • the current is parallel to the field lines • the current is at a 30 degree angle to the field lines • the current is at a 45 degree angle to the field lines • the current is at a 60 degree angle to the field lines • the current is perpendicular to the field lines**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, • the vector is aligned with the magnetic field • the vector is at a 30 degree angle to the magnetic field • the vector is at a 45 degree angle to the magnetic field • the vector is at a 60 degree angle to the magnetic field • the vector is perpendicular to the magnetic field