Chapter 4: Moving charges and magnetism Magnetic Force

What Is Magnetic Force?

If we place a point charge q in the presence of both a magnitude field given by magnitude B(r) and an electric field given by a magnitude E(r), then the total force on the electric charge q can be written as the sum of the electric force and the magnetic force acting on the object (Felectric + Fmagnetic ).

F = q E = q Q rˆ / (4πε0) r 2

Magnetic Field, Lorentz Force

Let us suppose that there is a point charge q (moving With a velocity v and, located at r at a given time t) in Presence of both the electric field E  and the magnetic Field B .The force on an electric charge q due to both of Them can be written as

F = q [ E  + v × B ] ≡ Felectric + Fmagnetic ).

MOTION IN A MAGNETIC FIELD
The force on a charged particle due to an electric field is directed parallel to the electric field vector in the case of a positive charge, and anti-parallel in the case of a negative charge. It does not depend on the velocity of the particle.
In contrast, the magnetic force on a charge particle is orthogonal to the magnetic field vector, and depends on the velocity of the particle. The right hand rule can be used to determine the direction of the force.
An electric field may do work on a charged particle, while a magnetic field does no work.
The Lorentz force is the combination of the electric and magnetic force, which are often considered together for practical applications.

MOTION IN COMBINED ELECTRIC AND MAGNETIC FIELDS
Lorentz Force
If the magnitudes of electric field strength and magnetic field strength are adjusted such that the magnitudes of the two forces are equal, then the net force acting on the charged particle is zero.
F = F(electric) + F(Magnetic) = q (E = v x B)
The below figure shows the representation of the electric field and the magnetic field along with the motion of charge when they are perpendicular to each other. F(electric) = F(Magnetic)

In the figure, we can clearly observe that the magnetic forces and electric forces are in opposite directions to each other.

Cyclotron
A cyclotron is a machine used to accelerate charged particles or ions to high energies.
To enhance the energies of charged particles, cyclotron uses magnetic as well as electric fields. It is called crossed fields since the magnetic and electric fields are perpendicular to each other. MAGNETIC FIELD DUE TO A CURRENT ELEMENT BIOT-SAVART LAW Assume that a conductor of a very large length L is carrying current I through it. The magnetic field due to the current, B is perpendicular to the plane of the conductor. Further, let us assume that a section of this conductor, say dL is producing a section of the magnetic field dB at point r away from it in the same plane. Let the angle between dL and dB in the direction of r be Θ.

MAGNETIC FIELD ON THE AXIS OF A CIRCULAR CURRENT LOOP 