We learned in lecture that the magnetic force on a charge q

Question

moving with velocity v in a magnetic field ~B has the form

F = q~v × B

One important fact about the cross-product is that for two vectors A and B , the following is
true A × B = −B × A which may also be determined by using the right-hand-rule. A convenient
way to calculate a cross-product is to decompose the vectors involved into x,y and z components,
and then use the following basic cross-product results for the basis vectors,

ˆx × ˆy = ˆz , ˆy × ˆz = ˆx , ˆz × ˆx = ˆy

Using the result just stated, the cross-products in the opposite order produce a minus sign,

ˆy × ˆx = −ˆz , ˆz × ˆy = −ˆx , ˆx × ˆz = −ˆy

so one only needs to remember the first three identities above, and these other identities can be
easily remembered. For this problem, use these identities to calculate the magnetic force on a
particle with a charge q = 7μC in a magnetic field B = (5 × 10−5 T)ˆy. Do the calculation for the
following three different velocities:

(a) v = v0ˆx

(b) v = v0ˆy

(c) v = v0 (x+y/suare root 2) where v0 = 5m/s