# Description of the motion of the COM of a system of charged particles moving in a magnetic field

I recently came across a problem where an electrically neutral particle is at rest in a uniform magnetic field. The particle now splits into two charged particles of equal mass $m$; charge and mass being conserved. Now, we know that if one particle has charge $q$, the other must have equal and opposite charge $-q$. It is said that the two particles collide after some time and we are asked to find that time.

My reasoning is that since the center of mass(com) of the system remains stationary, the particles will split in opposite directions to each other and thus collide just when each particle completes a semi-circle due to the magnetic force. With this approach, I get the answer right. Now let's forget the time period part and analyze the motion of the particles.

Second case: In analyzing the motion of the particles from a different perspective, we can say that throughout the motion, the center of mass must remain at rest as its charge is zero (q+(-q)=0) and so magnetic force is zero. So the charged particles must continue to move opposite to each other just so that the com remains stationary and not in a semi-circle. Perhaps the forces exerted on each other do the job. I am actually confused about the properties and motion of the com in situations involving charged particles in magnetic fields. I wonder whether there is a center-of-charge kind of concept where that point remains stationary when a neutral particle splits into two or more charged particles ? . Such a concept will simplify problem solving to a great extent in the same way the concept of com does.

Can someone please clarify these to me:

1. Why is the second case incorrect ?
2. Is there such a center-of-charge concept ?

Please feel free to edit and add relevant tags to the question.

• You draw not the full picture of what happens. What or who brakes the body in two pices? And what gives to them a motion? Without motion no influence of a magnetic field to charged particles. – HolgerFiedler Oct 4 '14 at 6:27
• I don't think you need the specifics of the splitting. I have written what happens after the splitting. The energy released from the splitting is used as kinetic energy by the particles and that causes the motion. – Gaurav Oct 4 '14 at 8:20