Question

Question: Given figure shows the paths of two particles circling in a uniform magnetic field. The particles have the same magnitude of the charge but opposite signs. (a)Which path corresponds to the more massive particle? (b)If the magnetic field is directed into the plane of the page, is the more massive particle positively or negatively charged?

Short answer

(a) The path with a bigger radius has a massive mass.

(b) The massive particle is positively oriented

Step-by-step solution

Radius of the circular path followed by charged particle

Radius of the circular path followed by the charged particle is given by,

$R=\frac{\sqrt{2mK}}{qB}$ (1)

Where R is radius of the particle, m is the mass of the particle,K is kinetic energy.

Finding the path corresponds to the more massive particle

From equation (1) we can see that radius of a particle is directly proportional to its mass.

So, the path with a bigger radius has a massive mass.

Finding whether the massive particle is positively or negatively charged the magnetic field is directed into the plane of the page

By using left hand rule which is says that,the thumb points in the direction of the magnetic force if the left hand's forefinger, middle finger, and thumb are all positioned perpendicular to one another.

Since the path with higher radius moves in a counter-clockwise direction and the magnetic field is directed into the plane of the page, the massive particle will be positively oriented.

Hence the massive particle is positively oriented.