# Bubble Chamber (for Charged Particles)

Charged particles passing through a bubble chamber leave tracks consisting of small hydrogen gas bubbles. These bubbles make visible the particles’ trajectories. In the diagram below, the magnetic field is directed into the page, and the tracks are in the plane of the page, in the directions indicted by the arrows.

a) Which of the tracks correspond to positively charged particles? Explain.

b) If all three particles have the same mass and charges of equal magnitude, which is moving the fastest? Explain.

c) If all three particles are moving with the same speed and have charges of equal magnitude, which has the greatest mass? Explain.

Magnetic force is

$F = q(v \times B)$

q is the charge, v is the speed, B is the field and x is the vector product.

The trajectories of the particles moving from left to right (West to East) are curved by the magnetic force.

$a =F/m = (q/m) (v \times B)$

and for rotation a is bigger (centripetal) for smaller curvature radius.

$F= m v^2/r = q v B$

this means

$r = m v/(q B) = p / (q B)$ (1)

a) Positively charged particles moving from left to right (from West to East) on the plane of the page and for B entering the page, ARE DEFLECTED UPWARDS

This is because (v x B). has the direction of a right screw that rotates to bring v parallel to B.

b) From relation (1) we can see that the greater the speed the greater the radius of curvature r of trajectory.

c) Greatest mass means smaller acceleration means larger curvature radius. This can be seen from relation (1).