Two very long wires are oriented parallel to the y axis and carry identical but
ID: 1541851 • Letter: T
Question
Two very long wires are oriented parallel to the y axis and carry identical but unknown currents I_a in opposite directions. The wires cross the x-axis at positions x = +2a and +3a. The wires produce a magnetic field at the origin with known magnitude B_0 and direction -z (i.e., into the page). Finally, a particle of charge q passes through the origin, with velocity v in the +y direction. a = 3.0 cm B_0 = 4.0 times 10^-6 T q = -50 mC v = 2.5 times 10^7 m/s I_a = ? Using the given magnitude and direction of the magnetic field B_0 at the origin, determine the current I_a. Bear in mind that I_a might be negative, indicating directions opposite to those shown in the figure. What is the force F on the charged particle as it crosses the origin?Explanation / Answer
A) Field at origin due to wire at x = 2a is B1 = mu_o*Ia/(2*pi*2a) = 2*10^-7*Ia/(2*0.03) into the page
Field at origin due to wire at x = 3a is B2 = mu_o*Ia/(2*pi*3a) = 2*10^-7*Ia/(3*0.03) out of the page
Bo = -B2+B1 = (-2*10^-7*Ia/(3*0.03)) + (2*10^-7*Ia/(2*0.03)) = 4*10^-6
Ia = 3.6 A
B) F = q*v*Bo*sin(90)
F = q*v*Bo = 50*10^-3*2.5*10^7*4*10^-6 = 5 N along +X-axis
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