P2213_HW12_solns_Fall2008

P2213_HW12_solns_Fall2008 - Physics 2213 HW#12 Solutions...

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- 1 - Physics 2213 HW #12 — Solutions Fall 2008 28.20 [Two Hikers] The magnitude of B a is given by Eq.(28.9) and the direction is given by the right-hand rule. (a) Viewed from above, the current is in the direction shown below. Directly below the wire the direction of the magnetic field due to the current in the wire is east. 7 5 0 800 A (2 10 T m/A) 2.91 10 T 2 5.50 m I B r μ π - - = = × = × (b) B from the current is nearly equal in magnitude to the earth's field, so, yes, the current really is a problem. 28.27 [Lamp Cord Wires] The lamp cord wires are two parallel current-carrying wires, so they must exert a magnetic force on each other. First find the current in the cord. Since it is connected to a light bulb, the power consumed by the bulb is P = IV . Then find the force per unit length using F / L = 0 2 I I r . For the light bulb, 100 W = I (120 V) gives I = 0.833 A. The force per unit length is F / L = 7 2 5 4 π 10 T m/A (0.833 A) 4.6 10 N/m 2 π 0.003 m - - × = × Since the currents are in opposite directions, the force is repulsive. This force is too small to have an appreciable effect for an ordinary cord. 28.37 [Coaxial Cable] To calculate the magnetic field at a distance r from the center of the cable, apply Ampere’s law to a circular path of radius r . By symmetry, (2 ) d B r = a a i B l for such a path. (a) For 0 encl 0 0 , 2 . 2 μ I a r b I I d μ I B π r μ I B π r < < = = = = a a i B l (b) For , r c the enclosed current is zero, so the magnetic field is also zero. A useful property of coaxial cables for many applications is that the current carried by the cable doesn’t produce a magnetic field outside the cable. 28.42 [Solenoid Design] At the center of a long solenoid 0 0 . N B nI I L = = 7 0 (0.150 T)(1.40 m) 41.8 A (4 10 T m/A)(4000) BL I N - = = = × The magnetic field inside the solenoid is independent of the radius of the solenoid, if the radius is much less than the length, as is the case here.

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- 2 - 1 [Two Wires] (a) The net magnetic field at the origin is zero . Using the right-hand rule, the magnetic field contribution due to wire #1 is in the +y direction, while the
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P2213_HW12_solns_Fall2008 - Physics 2213 HW#12 Solutions...

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