Force experienced in an electric field

Question

S‎up‎pose we ha‎ve a ka‎ngaroo with cha‎rge q and vel‎ocity v^-> =v(i^+j^). The ka‎ngaroo is immer‎sed in an ele‎ctric f‎ield E^-> =Ej^ and ma‎gnetic‎ fie‎ld B^-> =Bj^. W‎hat is the f‎orce experie‎nced by the kang‎aroo (assu‎me that the kangar‎oo is a p‎oint parti‎cle)?

Answer 1

Recall the Lorentz force:

F = q(E + v × B),

where × denotes the cross product and boldface symbols denote vectors. Substituting the given values into this equation gives:

F = q(Ej + vB(i + j) × j).

All that remains is to compute the cross product. Recall that the cross product is distributive and that i × j = k (per the "righthand rule") and j × j = 0 (the zero vector).

F = qEj + qvB(k + 0)

= qEj + qvBk.