Confusion regarding circular motion in a magnetic field If the velocity of a particle and magnetic field are perpendicular, force on the particle is also perpendicular to velocity. Suppose the force is along $x$ direction and velocity along $y$.
Then the initial component of velocity in the $y$ direction must be unchanged because acceleration is along $x$. So $v_x$ increases and $v_y$ is constant. But in circular motion, both $v_x$, $v_y$ change continuously. It's also said that charged particle moves in a circle in a magnetic field perpendicular to initial velocity.
Can someone resolve this confusion?
 A: 
But in circular motion, both vx, vy change continuously

That is not true. If you think about sinusoidal motion, there is a point during the motion that velocity does not change (that is, that the derivative is zero). That is exactly what happens at the point in the circular motion that you are talking about: If we imagine the motion to be counterclockwise, then as the particle arrives at the y=0 point, the y velocity has been increasing; after that point, it will be decreasing. But at that precise moment, it is neither increasing nor decreasing.
This can be shown mathematically as well: if we assume the orbit to have a radius R centered on the origin, and reaching (R,0) at t=0, we can write the position as:
$$x(t)=R\cos\omega t\\
y(t)=R\sin\omega t$$
Differentiating with respect to time, we find the velocity; differentiating again, we find the acceleration. And you will see the acceleration (change in velocity) in Y is zero at that precise point:
$$\begin{align}v_y(t)&=\omega R \cos\omega t\\
a_y(t)&=-\omega^2\sin\omega t\\
a_y(0)&=0\end{align}$$
