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Solutions4_2010

# Solutions4_2010 - Physics 205 Fall 2010 Problem set 4 1 Two...

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Physics 205. Fall 2010. Problem set 4. 1. Two insulated wires in the x-y plane cross at a 30 o angle but do not make electrical contact. Each wire carries 5.0 A current (the angle between current directions is 30 0 ). Find magnetic field in two non-equivalent points located 4.0 cm from the intersection, in the x-y plane, at equal distances from both wires. Hint: making a drawing will be very helpful. 24 points The non-equivalent points 4 cm from the intersection and at equal distances from both wires in the x-y plane are points A and C (did not use B to avoid confusion with the magnetic field). For point A I am not even bothering to calculate the shortest distance between this point and each wire. Using right-hand rule one can determine that contributions from both wires to the field at that point are directed in the opposite ways. Due to symmetry, they have same amplitudes, and therefore, the total field at point A is ZERO. For point C, the shortest distance between C and each wire is 4 cm sin75 0 = 3.864 cm. The field is then (factor 2 is due to two equal contributions from two wires adding up): T m A A Tm a I B 5 2 7 0 10 2 . 5 10 864 . 3 14 . 3 5 / 10 14 . 3 4 2 2 - - - = = = π μ Units can be just crossed out.

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