Motion in Combined Electric and Magnetic Fields

We know that whenever electric and magnetic fields act on a moving charge, the charge feels a force known as the Lorentz force, which is a vector quantity of forces owing to electromagnetic fields.

In the electromagnetic field, magnetic force and charge motion are mutually perpendicular, they are crossed fields, and forces owing to electric and magnetic fields operate in opposing directions.

Magnetic Fields

• The electrical charge particle generates an electric field perpendicular to the magnetic fields. The electric field is measured in volts per metre and a dimensionless number. We also know that the electromagnetic current is inherently conservative. 
• The magnetic field is the area surrounding a magnet where the magnetic force may be seen. The flow of electric charges creates this field. As a result, magnetic fields connect the magnetic lane’s direction. The electric fields are formed around the molecules, distinguished by their electric charges. 
• The force produced by an electric field is significantly greater than the force produced by a magnetic field. The circling motion of particles in a permanent magnet is used to calculate an atom’s mass. Magnetic field lines create a closed loop, but electric field lines do not form a loop.
• All charged particles use the Lorentz force to interact with electric radiation. Electrons in a magnetic field journey in a corkscrew pattern result from this interaction. According to special relativity, electrons should revolve with a single frequency around the conductive direction, known as the cyclotron resonance.

As a result, the Lorentz force F will be:

F=qE+qvB=q(E+vB)

When the intensity of the electric and magnetic fields is modified to equalise the forces due to the electric and magnetic fields (FE = FB), the charge can move freely in the field. E is equal to vB.

Therefore, v = E/B.

This exceptional situation is employed when charged particles with a specific velocity (of value E/B) must pass through the crossing fields undeflected, and this phenomenon is known as a frequency selector. In 1897, J.J.Thomson used it to calculate the charge-to-mass ratio.

This velocity selection principle is also utilised in mass spectrometers to identify charged particles based on their charge to mass ratio.

Motion of a Charged Particle in Combined Electric and Magnetic Field

In the context of the motion of a charged particle in a crossed electric and magnetic field, the angular momentum is parallel to the electron’s velocity. As a result, no effort is made, and there is no difference in the degree of acceleration. However, the direction of acceleration may shift. We’ll look at the speed of a photon beam in a magnetization that’s uniform. Consider the situation of v vertical to B first.

• The horizontal force, qvB, operates as a uniform circular motion, causing a circular motion parallel to the permanent magnet. If velocity has an element along with B, this fraction remains unaltered since motion along the magnetic field is unaffected.
• A charge particle’s velocity in both magnetic and electric fields. The result is a helical motion with a vastly increased pitch. 
• The diameter of each cyclical element and many other regular properties such as period, oscillation, and angular velocity are the same throughout the nonlinear travel of alpha particles parallel to a magnetic field. 

Applications: 

• Acceleration of charged particles which is a cyclotron.
• Measuring the specific charge of an electron which is according to the JJ Thomson experiment.
• Cyclotron

Force on a Current-Carrying Conductor in a Magnetic Field.

Theory:

A current-carrying conductor in a magnetic field feels a force. If the ground and current directions are perpendicular to one another, then the resultant force on the conductor will be perpendicular to both using Fleming’s rule.

When current flows through a conductor, it is displaced, indicating the presence of a force on the conductor.

Fleming’s Left-Hand Rule: Make a straight angle with your thumb and the first two fingers on your left hand. The thumb will point in the direction of force if the forefinger points in the direction of the field and the second finger in the direction of the current.

Conclusion

Charged particles have long been known to travel in circular orbits under a magnetic field. Magnetic fields are also utilised in accelerators for both scientific and medicinal applications to direct the travel of charged particles. The circling motion of charges in a magnetic field is used to calculate an atom’s mass.