MAGNETOSTATICS

Magnetostatics is a phenomenon that gives rise to a magnetic field due to a steady current. Like a charge creates an electric field surrounding it, similarly current produces magnetic field. In magnetostatics, this current is independent of time.

Biot savart law:

This law gives the value of magnetic field at a distance due to a current carrying wire. However, this law is valid only in magnetostatics.

Lorentz Force

Experiments show that force on a particle depends on position as well as velocity.

Electric force (F_e) on particle depends only on charge whereas magnetic force (F_m) depends on particle’s velocity. The direction and magnitude of F_m is depends on velocity. It is always perpendicular to velocity. Magnitude is proportional to the velocity component which is perpendicular to motion.

Total force on a charged particle is given by

F=F_e+F_m

F=qe+q(v X B)

This is valid for varying magnetic field also.

From this expression, it is clear that magnetic force acts on moving charges only.

Another feature is this force is perpendicular to velocity of the particle hence does no work at all. It only changes the direction of the velocity keeping the magnitude constant.

Magnetic field is represented by lines of vector B. Its density is proportional to the magnitude of B.

Gauss theorem:

The flux of B through a closed surface is zero.

From the expression, we conclude that lines of B have neither beginning nor end. Therefore, no. of magnetic field lines entering into the surface is equal to the no of field lines emerging out from it. This flux is independent of the shape of the body.

AMPERE'S LAW:

This law is applicable for steady current only.

If current is distributed over volume inside a current then it is written as-

APPLICATION OF THE THEOREM:

Magnetic field due to a straight current carrying conductor:

From the symmetry of the problem, we can draw a circular contour around the current carrying conductor since the magnetic field vector lines are circular in nature. The center of the circle lies at the axis of the wire.

Magnetic field due to a solenoid:

In solenoid, the magnetic field lines are directed along its axis. Hence we choose a rectangular contour to find the B.

Note: This law is useful only when the object has some symmetry associated with it. Otherwise, it becomes difficult to draw its contour.

FORCES ACTING ON A CURRENT LOOP:

According to ampere’s law, each charge in motion experiences a magnetic force. This force is transmitted to the conductor in which charges move. Therefore, conductor itself is acted upon by a force in the magnetic field.

This force is given by dF=I [dl X B], dl is the vector that has the same direction as that of the current.

They are also known as ampere forces.

Force between two current carrying wires (infinite):

Let us consider two infinite wires carrying current I₁ and I₂ respectively. Now, magnetic field due to wire I₁ is given by:

B=µ₀

Force per unit area on the other wire carrying current I₂ is given by:

This force is repulsive for antiparallel currents and attractive for parallel current. The direction of Magnetic field can be given by screw rule. Hence, this direction of the force can be predicted by applying vector rule only.

TORQUE ACTING ON A CURRENT LOOP:

Let us consider a loop carrying current 'I' in a uniform magnetic field. The resultant force acting on a closed loop in a uniform magnetic field is zero. Since resultant force is zero, body experiences no torque due to this magnetic force.

When the resultant force is not reduced to zero, the body experiences a torque whose magnitude is given by

P_m is the magnetic moment of current loop. P_m= IA, where A is the area of the surface.

DYNAMICS OF CHARGED PARTICLE IN MAGNETIC FIELD:

In uniform magnetic field, 3 paths are possible:

• Straight line path: when V_initial is parallel or antiparallel to magnetic field.
• Circular path: when V_initial is perpendicular to magnetic field.


MOTIONAL EMF:



This is the famous faraday's law.

Negative sign indicates it opposes the cause that produces it.

The direction of induced current is given by Lenz's law.

This is the domain of magnetostatics.

As we know, that steady current gives magnetic field which is static in nature likewise changing electric field also gives rise to magnetic field and this is non-static in nature.