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Magnetic Field Intensity and Point Charges

  1. Mar 8, 2007 #1
    1. The problem statement, all variables and given/known data

    Positive point charges q_1= 6.90 microC and q_2= 2.90 microC are moving relative to an observer at point P as shown in the figure. The distance from the observer to either charge is originally d = 0.190 m.The two charges are at the locations shown in the figure. Charge q_1 is moving at a speed of v_1 = 3.20×10^6 m/s and q_2 is moving at a speed of v_2 = 9.40×10^6 m/s.

    a. What is the magnitude of the net magnetic field they produce at point P ?
    b. What is the direction of the net magnetic field they produce at point P ?


    2. Relevant equations

    See below.

    3. The attempt at a solution
    I think I mixed up my signs for the cross product of v and r. Are the two fields in opposite directions? Any advice on those parts are appreciated.

    B_1 = (mu_0/4*pi)*[(q*v vector*r vector)/(r^3)]

    v vector = 3.20*10^6 m/s*i
    r vector = (-0.190 m)*j

    v vector*r vector = (3.20*10^6 m/s)i*(-0.190 m)j = -60800 m^2/s*k

    B_1 = [(1*10^-7 T*m/A)*(6.90*10^-6 C)(-60800 m^2/s*k)]/[0.190 m]^3

    = (-6.12*10^-5 T)*k ??

    B_2 = (mu_0/4*pi)*[(q*v vector*r vector)/(r^3)]

    v vector = -9.40*10^6 m/s*i
    r = 0.190 m*j

    v vector*r vector = (-9.40*10^6 m/s*i)*(0.190m*j) = -1786000 m^2/s

    B_2 = [(1*10^-7 T*m/A)*(2.90*10^-6 C)(-1786000 m^2/s*k)]/[0.190 m]^3
    = (-7.55*0^-5 T)*k ??

    B_total = (-6.12*10^-5 T)*k - (-7.55*0^-5 T)*k = -(1.37*10^-4 T)*k out of the page?? (negative z-axis?)

  2. jcsd
  3. Mar 8, 2007 #2
    Can anyone please check over my workings, particularly my signs?

    Thank you very much.
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