Two very long thin straight wires running parallel to the z-axis and cutting thr
ID: 1610192 • Letter: T
Question
Two very long thin straight wires running parallel to the z-axis and cutting through the y-axis at y_1 = 4m and through the x-axis at x_2 = am, respectively, carry currents I_1 and I_2, both in the -z-direction, as shown in drawing below, I_1 is 6 times as strong as I_2. The two currents produce magnetic field contributions B_1 and B_2, respectively, at point P (5m, 4m, 0m) in the x - y-plane. (a) What is the absolute value of the angle between the +x-direction and the total magnetic field vector, B = B_1 + B_2, produced by the two currents at point P? (b) If the total magnetic field strength at point P is B |B| = 4.8 muT what are I_1 and I_2? (c) Suppose an electron is shot through point P in the -z-direction with a speed of 3.6 times l0^5 m/s. Find the electron's acceleration vector, a (a_z, a_y, a_z, ) at P, due to the magnetic force. State all three cartesian components of a.Explanation / Answer
Let x = 5 m, y = 4 m
I2 = 6*I1
a) at point P,
B1 = mue*I1/(2*pi*x) (towards -y axis)
B2 = mue*I2/(2*pi*y) (towards +x axis)
angle made resulatnt magnetic field with +x axis,
theta = tan^-1(B1/B2)
= tan^-1(I1*y/(I2*x)
= tan^-1(I1*5/(6*I1*4)
= tan^-1(5/24)
= 11.8 degrees below +x axis
b)
Bnet = sqrt(B1^2 + B2^2)
Bnet^2 = B1^2 + B2^2
(4.8*10^-6)^2 = (4*pi*10^-7*I1/(2*pi*5))^2 + (4*pi*10^-7*6*I1/(2*pi*4))^2
==> I1 = 15.8 A
I2 = 6*I1
= 6*15.8
= 94.8 A
c) use, F = q*v*B*sin(90)
m*a = q*v*B
a = q*v*B/m
= 1.6*10^-19*3.6*10^5*4.8*10^-6/(9.11*10^-31)
= 3.03*10^11 m/s^2
ax = a*sin(11.8)
= 3.03*10^11*sin(11.8)
= 6.20*10^10 m/s^2
ay = a*cos(11.8)
= 3.03*10^11*cos(11.8)
= 2.97*10^11 m/s^2
az = 0
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