An alpha-particle moves through a uniform magnetic field whose magnitude is 1.5 T. The field is directly parallel to the positive z-axis of the rectangular coordinate system. What is the magnitude of the magnetic force on the alpha-particle when it is moving with a velocity v = (2 i - 3 j + 1 k) x 10⁴ m/s ?

3.7 X 10^-14 N

F = q.(v X B)

v = (2 i - 3 j + 1 k) x 10⁴ m/s ⇒ |v| = \(\sqrt { 2^{2} + 3^{2} + 1^{2}}\) x 10⁴ m/s  = \(\sqrt {15}\) x 10⁴ m/s ;

B = 1.5 T ;

q = 4 e = 4 x 1.6 x 10^-19 C = 6.4 x 10^-19 C 

F = 3.7 X 10^-14 N