Two very long wires arc oriented parallel to the y axis and carry identical but
ID: 1544361 • Letter: T
Question
Two very long wires arc 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^-6T q = -50 mC v = 2.5 times 10^7 m/s I_a = ? Using the given magnitude and direction of the magnetic field B^rightarrow_0 at the origin, determine the current I_a. Bear in mind that h might be negative, indicating directions opposite to those shown in the figure. What is the force F^vector on the charged particle as it crosses the origin?Explanation / Answer
a) we know,
Bo = mue*I1/(2*pi*d1) - mue*I2/(2*pi*d2)
Bo = mue*Ia/(2*pi*2*a) - mue*Ia/(2*pi*3*a)
Bo = mue*Ia/(2*pi*a)*(1/2 - 1/3)
Bo = mue*Ia/(12*pi*a)
Ia = Bo*12*pi*a/mue
= 4*10^-6*12*pi*0.03/(4*pi*10^-7)
= 3.6 A
b) |F| = q*v*B*sin(theta)
= 50*10^-3*2.5*10^7*4*10^-6*sin(90)
= 5 N (towards +x axis)
in vector notation, F = 5 N i
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