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Find B using cross product

  1. Oct 6, 2007 #1
    1. The problem statement, all variables and given/known data
    find B from F=q(v X B), where F is magnetic force, q = charge, v = velocity, B = magnetic field.

    Carrying out 3 experiments, we find that if
    v_1 = i, (F/q)_1 = 2k - 4j
    v_2 = j, (F/q)_2 = 4i - k
    v_3 = k, (F/q)_3 = j - 2i

    where i,j,k are the unit cartesian vectors

    This is the problem 1.4.16 from Arfken's Mathematical methods for physicists

    3. The attempt at a solution

    I tried adding the v's and F's as follows:
    [(v_1 X B)+ (v_2 X B) +(v_3 X B)] = - [(B X v_1)+ (B X v_2) +(B X v_3)] = -[B X (v_1 + v_2 + v_3)] = [(F/q)_1 + (F/q)_2 + (F/q)_3]
    => -[B X (i + j + k)] = [(2i - 4j) + (4i - k) + (j - 2i)] = 2i - 3j + k
    => [B X (i + j + k)] = -2i + 3j - k

    multiplying out the cross product, I got: [B X (i + j + k)] = (B_y - B_z)i - (B_x - B_z)j + (B_x - B_y)i
    => B_y - B_z = -2
    B_x - B_z = -3
    B_x - B_y = -1

    and this gives infintely many solns for B_x, B_y, and B_z

    is this correct? or did I screw up somewhere?
     
    Last edited: Oct 6, 2007
  2. jcsd
  3. Oct 6, 2007 #2

    D H

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    Since v_1 = i, how can F_1 = q(v_1xB) have any component in the i direction?
     
  4. Oct 6, 2007 #3
    typo on my part
     
  5. Oct 7, 2007 #4
    come on, can't someone help me?
     
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