Motion in Magnetic Field: Class 12 Notes, Definition, Working Principle, Examples & Real-Life Applications

Motion of charged particle in magnetic field is all about movement of particle based on the force exerted on it. When an electric current passes through the conductor, a magnetic field is generated around it.  

Now, when a charged particle moves in the magnetic field, it will feel force, which might change its direction. The magnetic force will be exerted on charged particle if it is moving else no force will be affecting the particles. 

Thus, the force is always toward the motion, it will change the direction of charged particles rather than slowing or boosting its speed. 

If the charge particle is moving perpendicular to the magnetic field, then the particle will be in circular path. Here, the magnetic force is acting like a centripetal force, which keeps pulling towards the Centre of circle. 

Now, in case, the charged particle moves in the magnetic field along with an angle, its motion will be along or across the field line. Due to these two motions, the particle will move in a spiral shape.  

Why is it important? 

The behavior of charged particles in magnetic field help in various ways such as: 

• Understanding the space weather 

• Building electric motors 

• Guiding particles in scientific instruments 

Motion of charged particles in magnetic fields are numerous practical and scientific. 

• Medical Application 

• Magnetic Resonance Imaging (MRI) 

• Medical Isotope Production 

• Radiation Therapy 

• Technological Applications 

• Magnetrons 

• Hall Effect Sensors 

• Cathode Ray Tubes (CRTs) - Older Technology 

• Understanding Natural Phenomena 

• Cosmic Ray Deflection 

• Aurora Borealis and Australis (Northern and Southern Lights) 

• Van Allen Radiation Belts 

Note :

•  w, f, T are independent of velocity.

If the velocity of the charge is not perpendicular to the magnetic field, we can break the velocity in two components – v_||, parallel to the field and v, perpendicular to the field. The components v_|| remains unchanged as the force $q\vec{v}\times \vec{B}\mathrm{}\mathrm{}$ is perpendicular to it. In the plane perpendicular to the field, the particle traces a circle of radius $\mathrm{r}\mathrm{}=\mathrm{}\frac{m{v}_{\perp }}{qB}$  as given by equation. The resultant path is helix.

Let a particle have initial velocity in the plane of the paper and a constant and uniform magnetic field also in the plane of the paper.

The particle starts from point A₁.

It completes its one revolution at A₂ and 2^nd revolution at A₃ and so on. X-axis is the tangent to the helix

A₁, A₂, A₃, ..........all are on the x-axis.

distance         A₁A₂ = A₃A₄ = ............... = v cosΘ. T = pitch

where             T = Time period

Let the initial position of the particle be (0, 0, 0) and v sin Θ in +y direction. Then in x :

F_x = 0, a_x = 0, v_x = constant = v cosΘ, x = (v cosΘ)t

Below is an example of motion in magnetic field.  

• Helical Motion in a Uniform Magnetic Field 

• Motion in a Cyclotron 

• Electron Beam in a Television (CRT - older technology) 

• Mass Spectrometer 

• Circular Motion in a Uniform Magnetic Field