PY208-Lecture-19 - Physics 208N-004 Lecture #18 23 February...

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1 Physics 208N-004 Lecture #18 – 23 February 2011 Chapter 28: 4-5 – Ampere’s Law, Solenoid and Toroid Review Chapter 28: 1-3 Definition of Amp and Coulomb F / l = ( o /2 ) ( I 1 I 2 /d ) = [(4 x 10 -7 Tm/A )/(2 )] x [(1 A )(1 A )] /(1 m ) = 2 x 10 -7 N/m F 2 = I 2 B 1 l 2 F 1 = I 1 B 2 l 1 μ 0 = 4 π x 10 -7 T·m/A. B proportional to I and inversely to r Parallel currents attract; antiparallel currents repel. 28-2 Force between Two Parallel Wires Example 28-4. Force between two current- carrying wires. The two wires of a 2.0-m-long appliance cord are 3.0 mm apart and carry a current of 8.0 A dc. Calculate the force one wire exerts on the other. F 2 = I 2 B 1 l 2 F 1 = I 1 B 2 l 1 Read these equations properly
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2 28-3 Definitions of the Ampere and the Coulomb The ampere is officially defined in terms of the force between two current-carrying wires: One ampere is defined as that current flowing in each of two long parallel wires 1 m apart, which results in a force of exactly 2 x 10 -7 N per meter of length of each wire. The coulomb is then defined as exactly one ampere-second. F / l = ( o /2 ) ( I 1 I 2 /d ) = [(4 x 10 -7 Tm/A )/(2 )] x [(1 A )(1 A ) / (1 m )] = 2 x 10 -7 N/m Ampère’s law relates the magnetic field around a closed loop to the total current flowing through the loop: 28-4 Ampère’s Law This integral is taken around the edge of the closed loop.
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3 28-4 Ampère’s Law Using Ampère’s law to find the field around a long straight wire: Use a circular path with the wire at the center; then B is tangent to dl at every point. The integral then gives so B = μ 0 I /2 π r , as before. B   28-4 Ampère’s Law Example 28-6: Field inside and outside a wire. A long straight cylindrical wire conductor of radius R carries a current I of uniform current density in the conductor. Determine the magnetic field due to this current at (a) points outside the conductor ( r > R ) and (b) points inside the conductor ( r < R ). Assume that r , the radial distance from the axis, is much less than the length of the wire. (c) If R = 2.0 mm and I = 60 A, what is B at r = 1.0 mm, r = 2.0 mm, and r = 3.0 mm?
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4 28-4 Ampère’s Law Conceptual Example 28-7: Coaxial cable. A coaxial cable is a single wire surrounded by a cylindrical metallic braid. The two conductors are separated by an insulator. The central wire carries current to the other end of the cable, and the outer braid carries the return current and is usually considered ground. Describe the magnetic field (a) in the space between the conductors, and (b) outside the cable.
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PY208-Lecture-19 - Physics 208N-004 Lecture #18 23 February...

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