ABSTRACT
Employ the geometric expression of the cross product to evaluate each of the following: (a) ıˆ× kˆ, (b) ~r ×→F
b , (c) ~r ×→F
c , (d) ~v ×→B .
L.2 Evaluate the cross products in L.1 using component expressions. L.3 Compute (a) cross and (b) dot products for the following pairs of [3-d] vectors: (i) 13 [ in the xy-plane, at 22.62◦ anti-clockwise w.r.t. x− axis ],
5 [ in the xy-plane, at 53.13◦ anti-clockwise w.r.t. y − axis ], (ii) (12 , 5 , 0), (−4 , 3 , 0), and (iii) 6 [ ↓ ], 5 [ → ]. L.4 A constant magnetic field, →B
0 = B0 [⊙ ], is found to exist in a region of space. A
particle with mass M and charge q is moving with velocity ~v = v‖ [⊙] + v⊥ [→] within this region at some time t. Compute the magnitude of the component of the magnetic force acting on the particle in the direction of its velocity at this instant.
