How to find the period in magnetic uniform field

How to find the period in magnetic uniform field

Magnetic field is the special type of matter arising around moving charged particles. The simplest way of its detection consists in use of a magnetic needle.


1. Magnetic field is non-uniform and uniform. In the second case of its characteristic are as follows: lines of magnetic induction (that is the imagined lines in which direction the magnetic needles placed in the field are located) represent parallel straight lines, the density of these lines is identical everywhere. Force with which the field uses on a magnetic needle is also identical in any point of the field, both in size, and in the direction.

2. Sometimes it is necessary to solve a problem of definition of the period of a turnover of charged particle in uniform magnetic field. For example, the particle with a charge of q and mass of m flew in uniform magnetic field with induction In, having the initial speed of v. What period of its turn?

3. Begin the decision with search of the answer to a question: what force affects a particle at present? It is the Lorentz force which is always perpendicular to the direction of the movement of a particle. Under its influence the particle will move on r radius circle. But the perpendicularity of vectors of Lorentz force and speed of a particle means that work of Lorentz force is equal to zero. Means, both the particle speed, and its kinetic energy at the movement on a circular orbit remain constants. Then the size of Lorentz force is constant, and is calculated on a formula: F = qvB

4. From other party, the radius of a circle on which the particle moves is connected with the same force such ratio: F = mv^2/r, or qvB = mv^2/r. Therefore, r = vm/qB.

5. The cycle time of charged particle on a circle of radius of r is calculated on a formula: T = 2πr/v. Substituting the value of radius of a circle defined above in this formula, you receive: T = 2πvm/qBv. Having reduced the identical size of speed in numerator and a denominator, receive final result: T = 2πm/qB. The task is solved.

6. You see that at rotation of a particle in uniform magnetic field the period of its address depends only on the size of magnetic induction of the field and also a charge and mass of the particle.

Author: «MirrorInfo» Dream Team