Fall 2011 Homework 12 Solutions

# Fall 2011 Homework 12 Solutions - Physics 21 Fall 2011...

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Physics 21 Fall, 2011 Solution to HW-12 27-36 A straight, vertical wire carries a current of I = 1 . 19 A downward in a region between the poles of a large superconducting electromagnet, where the magnetic field B has a magnitude of B = 0.591 T and is horizontal. What are the magnitude and direction of the magnetic force on a section of the wire with a length of l = 1 . 00 cm that is in this uniform magnetic field, if the magnetic field direction is (a) east, (b) south, (c) 34 south of west? The diagram shows the view looking down in the direction of the current, for an arbitrary orientation of B in the hori- zontal plane: N E S W B F mag I We use the right hand rule to evaluate the magnetic force F mag = I l × B , where l is a vector of length l , the length of the wire section, that points in the direction of the current. One can see that for any horizontal B , the magnetic force will also be horizontal, and its direction will be 90 clockwise from B . (a) For B pointing east, the magnitude of F mag is F mag = IlB = (1 . 19 A)(0 . 010 m)(0 . 591 T) = 7 . 03 mN and the direction is south. (b) For B pointing south, F mag is the same as in part (a), and the direction of F mag is west. (c) For B pointing east, F mag is the same as in part (a), and the direction of F mag is 34 west of north.

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