Magnetic Force on a moving charge in uniform magnetic fields

A magnetic field is a vector field that describes the magnetic effect on moving electric charges, electric currents and magnetic substances. A mobile charge in a magnetic field experiences a force perpendicular to the velocity of the mobile charge and to the magnetic field.

 A permanent magnet’s magnetic field pulls on ferromagnetic substances along with iron, and attracts or repels different magnets. In addition, a magnetic field that varies with area will exert a force on a variety of non-magnetic substances through affecting the movement in their outer atomic electrons. Magnetic fields surround magnetised substances, and are created by electric powered currents along with the ones utilised in electromagnets, and by electric powered fields varying in time.

Units of Magnetic Field

The SI unit for magnetic field is Tesla (T). It is derived from the magnetic part of Lorentz force law,

Fmagnetic=qv B

Where

q=charge

v=velocity of charge

B=magnetic field

Magnetic field is symbolised by “B”.

Magnetic Force

If we place a unit charge q withinside the presence of both a magnitude field given with the aid of using value B(r) and an electric powered field given with the aid of using a value E(r) ,then the entire force on the electrical charge q may be written as the sum of the electrical force and the magnetic force being experienced by the object (Felectric+Fmagnetic).

Magnetic fields can exert a force on electric powered charge only if it’s far shifting, just as a shifting charge produces a magnetic field. This force will increase with both an increase in charge and magnetic field strength. Moreover, the force is more while charges have better velocities.

Formula of Magnetic  Force

The value of the magnetic force relies upon how much charge is in how much movement in each of the items and the distance between the items.

The magnetic force can be expressed as:

F=q[E(r)+vB(r)]

This force is called the Lorentz Force. It is the mixture of the electrical and magnetic force on a unit charge because of electromagnetic fields. The interaction among the electrical field and the magnetic field has the subsequent features:

The magnetic force relies upon the charge of the particle, the rate of the particle and the magnetic field wherein it is placed. The path of the magnetic force is contrary to that of a positive charge.

The value of the force is calculated through the cross product of velocity and the magnetic field, given through q [ v × B]. The resultant force is therefore perpendicular to the path of the velocity and the magnetic field, the path of the magnetic field is anticipated through the right-hand thumb rule.

If the charge is static, the net magnetic force is zero.

Force Due to Electric Field

The force due to the electrical field on a charge is constructed into its definition. It constantly acts either parallel or antiparallel to the electrical field and is unbiased of the rate of the charge. This way it has the capacity to do work and impart energy to the charge.

Fe=qE

Where 

q= charge

E= electric field

Lorentz Force

When a charge travels via both an electric powered and magnetic field, the total force at the charge is referred to as the Lorentz force. It is truly the sum of the magnetic and electric powered forces:

F=Fe+Fm

F=qE+qvB

F=q(E+vB)

Combinations of electrical and magnetic fields are utilised in particle accelerators, cyclotrons and synchrotrons. The magnetic field may be used to maintain the charges transferring in a circle whilst the electrical field is used to boost up the charges and impart them energy.

Magnitude of the Magnetic Force

The magnitude of magnetic force on a charged particle q in the magnetic field B having a velocity v with an angle with the magnetic field B is given by:

F=qv Bsin

Motion of a charge in uniform magnetic field

We will now consider, in more detail, the movement of a charge moving in a magnetic field. We have learnt in Mechanics that a force on a particle does work if the force has a factor along (or opposed to) the path of movement of the particle.

 In the case of movement of a charge in a magnetic field, the magnetic force is perpendicular to the velocity of the particle. So, no work is done and no change in the value of the velocity is produced (though the path of momentum can be changed). [Notice that this is in contrast to the force due to an electric powered field, qE, which could have a factor parallel (or antiparallel) to movement and as a result can transfer energy in addition to momentum.]

We shall consider movement of a charged particle in a uniform magnetic field. First consider the case of v perpendicular to B . The perpendicular force,qvB , acts as a centripetal force and produces a circular movement perpendicular to the magnetic field. The particle will describe a circle if v and B are perpendicular to each other.

If velocity has a factor alongside B, this factor stays unchanged as the movement alongside the magnetic field will now no longer be affected by the magnetic field. The movement in a plane perpendicular to Bis as before a circular one, thereby generating a helical movement.

You have already learnt in previous topics that if r is the radius of the circular path of a particle, then a force of mv2/r , acts perpendicular to the path towards the centre of the circle, and is referred to as the centripetal force. If the velocity v is perpendicular to the magnetic field B, the magnetic force is perpendicular to each v&B and acts like a centripetal force. It has a value qvB. Equating the two expressions for centripetal force,

mv2/r=qvB

r=mv/qB

or the radius of the circle described by the charged particle.

Properties of Magnetism

All magnets have poles: the North Pole and the South Pole. Magnets attract ferromagnetic substances which include iron, nickel, and cobalt. The magnetic force of a magnet is stronger at its poles than in the middle. A freely suspended magnet remains constantly positioned in the North-South direction. The different forms of magnet are: Permanent and Temporary magnets. Permanent magnets stay magnetised even without the impact of the outside magnetic field. While, temporary magnets lose their magnetism whilst eliminated from the outside magnetic field, which include an iron pin.

Conclusion

Magnetic fields exert forces on charged particles in motion. The route of the magnetic force F is perpendicular to the plane shaped with the aid of using v and B as decided with the aid of using the right-hand rule. 

The SI unit for magnitude of the magnetic field power is referred to as the tesla (T), that is equal to at least one Newton per ampere-metre (N/A-m). When the expression for the magnetic force is mixed with that for the electrical pressure, the mixed expression is referred to as the Lorentz force.