# Homework Help: Magnetic field problem

1. Mar 31, 2005

### sinas

I don't even know where to begin here, could use a hint =/

"Two positive ions having same charge q but different masses, m1 and m2, are accelerated horizontally from rest through a potential difference V. They then enter a region where there is a uniform magnetic field B normal to the plan of the trajectory. Show that if the beam entered the magnetic field along the x-axis, the value of the y-coordinate for each ion at any time t is approximately y=Bx^2(q/8mV)^1/2 provided y remains much smaller than x. "

2. Apr 2, 2005

### Andrew Mason

You would use the Lorentz force equation:

$$\vec F = ma\hat j = q v\hat i \times B\hat k = qvB\hat j$$

Determine speed v from $$qV = E = \frac{1}{2}mv^2$$

Since a is in the direction perpendicular to v, it is in the direction of the y axis. So the distance moved in the y direction is

$$y = \frac{1}{2}at^2$$

and t = x/v

That should enable you so solve this problem.

AM