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The magnetic field is the region in which the influence of magnetism may be felt around a magnet. The magnetic field is a tool that we use to explain how magnetic force is dispersed in the space surrounding and within magnetic objects in nature.
The Motion Of A Charged Particle In An Magnetic Field
When a force acts on a particle, it is said to produce work if a portion of the force is directed in the particle’s direction of travel. The magnetic force is applied parallel to the surface to the particle’s motion in a magnetic field under study when we have a stream of electrons bearing a charge q travelling in a uniform magnetic field of size B.
In this case, we claim that the magnetic force does not work on the particle, and therefore no change in the electron’s velocity can be seen. When the electron’s velocity v is parallel to the electromagnet, we may write,1
In this case, the magnetic movement is caused towards the object’s centre of circular motion in a magnetic field and operates as angular momentum. As a result, if v and B are perpendiculars, the component describes a circle.
Applications
The following are some of the key applications related to the existence of the two fields:
- A charged particle’s motion in a magnetic field
- An electron’s particular charge is measured (J.J.Thomson experiment)
- Alpha particles acceleration (cyclotron)
- Examples of Solved Problems
In a gravity-free environment, a charged particle travels without changing velocity. Which of the following is/are viable options?
- A) B = 0, E = 0 B) E = 0, B ≠ 0 C) E ≠ 0, B = 0 D) B ≠ 0, E ≠ 0
If a heavy ion travels in a gravity-free environment without changing velocity, then
Particles can travel in any orientation with constant velocity. As a result of B = 0 and E = 0, the particle can travel in a compound pendulum. The vertical component, which causes particles to move in a round, will be provided by an electromagnet.
If qE = QB and the magnetic and electric forces are in opposing directions, the particle will travel at a uniform speed.
The Motion Of A Charged Particle In The Uniform Magnetic Field
Lorentz Force
Suppose the amplitude of the motion of a charged particle in a uniform magnetic field is modified so that the measured values of the two forces are identical. In that case, the net pressure applied on the free electron is zero.
F = F(Electronic) + F(Magnetic) = q (E = v x B)
Lorentz force is experienced by moving charges when they come into contact with electrical and magnetic fields. Lorentz force is a type of force that may be computed as the weighted combination of capacitive and inductive field forces.
F(electric) = F(Magnetic)
We can easily see that the electromagnetism forces are pointing in the reverse direction. When the constants of E and B are modified precisely so that the intensity of the two forces is equivalent, the total pressure exerted on the full control is zero, and the particles travel influx in the field.
Net Force Equals Zero
When the intensity of the electric and magnetic fields is modified to equalize the forces associated with the electromagnetic force (FE = FB), the charge can move freely in the field.
qE=Bqv, E=Bv, v=E/B
This instance is employed when alpha particles of another velocity (E/B) are used to transit undeflected between the crossing fields. This is referred to as a velocity selector. In 1897, J. Thomson used it to calculate the charge-to-mass ratio.
The velocities selector is used in mass spectrometers to identify charged particles based on their price-to-performance ratio.
Difference between circular and helical motion
Here is the quick difference between circular and helical motion
Circular Motion refers to the movement of an object at a constant speed in a circular path. The velocity of this moving object changes during each movement as the direction is constantly changing, however the speed is constant.
Helical motion refers to the motion which is produced in case the single component of the velocity remains the same in direction and magnitude whereas the other component remains the same in speed.
Cyclotron
A cyclotron is a device that uses high energy to accelerate electromagnetic waves or ions. Cyclotrons employ both magnetic and electric fields to boost the energy of charged particles. Because the electromagnetism fields are parallel to one another, it is referred to as crossed forces.
The Motion Of A Charged Particle In Crossed Electric And Magnetic Field
In the context of 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 done and there is no difference in the degree of the 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, q v B, 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 by it.
- A chargeable 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 case of nonlinear travel of alpha particles parallel to a magnetic field.
Suppose a percentage of the particle’s velocity corresponds to the magnetic field (notated by v2). In that case, the electron will move with both the ground, and the particle’s route will be sinuous. Ground p is the distance traversed along with the permanent magnet in one revolution. p = v2T = 2mv2/2Qb
Conclusion
When a force acts on a particle, it is said to produce work if a portion of the force is directed in the particle’s direction of travel. The magnetic force is applied parallel to the surface to the particle’s motion in a magnetic field under study when we have a stream of electrons bearing a charge q travelling in a uniform magnetic field of size B.
