Motion of a charge in a magnetic field

[harini_5]

A particle of charge q and mass m starts its motion from origin with u=a i.A uniform B=b/4 i + (sin 60)/2 j exists everywhere in space.Find the component of velocity in y direction when z coordinate of it becomes maximum

Sir, if I find the magnetic force,Its component is 0 in Y direction.With no force acting in Y direction ,how come its velocity changes??

then I thought that

I'm missing one step:the force is in z direction initially but when it starts going in a circular motion then the x component of the field will cross with velocity and produce a force which has a component in y direction.
please help me!

thanks in advance

 

[gabbagabbahey]

Treat your velocity as some unknown function of time: \vec{u}(t)=u_x(t)\hat{i}+u_y(t)\hat{j}+u_z(t)\hat{k}. Then use the expression for the magnetic field and the Lorentz force law to find the equation of motion for the particle. Then solve that differential equation for \vec{u}(t) and plug in the initial condition \vec{u}(0)=a\hat{i}. Finally, find where the maximum of the z-component occurs.