Motion of a particle in a magnetic field.
The only force acting on a particle with charge e and velocity v, in a constant magnetic field B, is ev × B. Also, r(0)=0 and .
I've shown that:
Now the question asks to find equations for the path of the particle if B=(B,0,0) , V=(v_1,v_2,0) and r=(x,y,z).
I evaluated the cross product and equated the components to get:
By solving the second and third equations, I generate equations involving exponentials but the answer has equations involving sin and cos.
Can someone see where I've gone wrong? Thanks in advance.