Magnetic Dipole and Magnetic Flux

Magnetic dipole is an important topic of IIT JEE Physics. The topic becomes all the more significant because it fetches some direct questions in the JEE. It is very interesting and can be mastered easily with little effort. We discuss here the concepts of magnetic dipole and magnetic flux in detail.

Magnetic Dipole

The limit of a closed loop of electric current is defined as a magnetic dipole. The structures, which tend to align along the direction of magnetic field, are known as magnetic dipoles. A current loop creates as well as responds to magnetic fields. We first examine the torque felt by a dipole in a magnetic field. Consider the current loop in a magnetic field in the figure given below. The two forces which are equal and opposite do not act to bring about a movement in the dipole, but only rotate it.   


Magnetic Dipole

The moment arm for the torque denotes the height of the dipole i.e. h sin q. The angle between the direction of the magnetic field and a vector which is normal to τ dipole lies exactly in a horizontal plane as shown in the picture above. It can be seen that the torque always attempts to reduce the angle q to zero. This is the time when the potential energy is at its minimum. The torque and potential energy are:

τ = IAB sin θ      and U= -IAB cos θ,

here A denotes the area of the loop of the dipole. And the product IA denotes the dipole moment.

Examples: Magnetic compass needles and bar magnets are examples of macroscopic magnetic dipoles. Current carrying solenoid, current carrying coil, current loop, etc. are the other examples.

Magnetic Dipole Moment:

Magnetic dipole moment is the measure of the ability of a dipole to convert itself and come into alignment with a given external magnetic field. It may also be defined as the maximum expanse of torque caused by magnetic force on a dipole that ascends per unit value of surrounding magnetic field in vacuum. In case of a uniform magnetic field, the magnitude of the dipole moment is proportional to the maximum quantity of torque on the dipole. This generally occurs when the dipole is at right angles to the magnetic field.

Remarks:

(1) It is not possible to separate out the two poles of a magnet.

(2) Magnetic dipole is not a system composed of two poles because the existence of monopoles is not possible.

(3) A loop of single turn is also a magnetic dipole. One face of the loop behaves as North Pole and the other face behaves as South Pole. The face of the coil, in which current is anticlockwise, behaves as north pole and the face in which current is clockwise, behaves as south pole.

Magnetic flux

The number of lines of force passing through a given area is called the magnetic flux. It also denotes the magnetic field passing through a given surface such as a conducting coil. The magnetic flux passing through unit normal area is defined as magnetic induction (B).

When the magnetic field is normal to the plane then
Φ = BA, when A = 1m2 then Φ = B.

 


Magnetic Flux

When magnetic field makes an angle θ with the normal to the plane:

In such a case:

(i) Magnetic flux linked with the plane = Area of the plane

      (A) × Component of magnetic field normal to the plane (B cos θ) 

      i.e. Φ= AB cos θ If the number of turns in the coil is N. then Φ = NAB cos θ

 


Magnetic field makes an angle θ with the normal to the plane


(ii) Φ = magnetic field normal to the plane (B) × component of A in the direction of magnetic field (A cos θ)

      i.e. Φ = BA cos θ

Calculation of magnetic field

In both cases q is the angle between B and n (here vectors are denoted in bold letters)

(iii) When they are mutually parallel then θ = 0o and Φ = BA.

(iv) When they are mutually perpendicular, θ= 90o and Φ = 0.

(v) When are antiparallel, then θ = 180o and Φ = BA.

(e) When the angle between B and the plane of coil is θ then Φ= BA sin θ.



  • If the number of turns in the coil is N then Φ = NBA sin θ.
Magnetic field of coil

(i)When the plane of coil is parallel to then θ = 0o and Φ = 0.

(ii) When and the plane of coil are mutually perpendicular i.e. θ = 90,    then Φ = BA.

(iii) When and the plane of coil are mutually antiparallel i.e. θ = 180o, then Φ = 0.

(f) Magnetic flux linked with a small surface element dA dΦ = B.d

 Or A = BdA cos θ

where d A = area of small element.

                 = unit normal vector.

                                                     
Magnetic flux linked with a small surface element

     (g) The flux linked with total area of the surface A





You may also view the video on magnetic flux 

(h) Positive magnetic flux: When the magnetic induction B¯ and the unit normal vector are in the same direction then Φ is called the positive magnetic flux.

                         —> B

                         —> A

                         Φ = BA

(i) Negative magnetic flux: When the magnetic induction B¯ and unit normal vector are mutually in opposite directions then Φ is called negative magnetic flux

                        Φ = – BA

(j) The flux emanating out of a surface is positive and the flux entering the surface is negative.

(k) Φ is a scalar quantity.

(l) The net magnetic flux coming out of a closed surface is always zero, i.e.





Illustration of Magnetic flux


The contribution to magnetic flux for a given area is equal to the area times the component of magnetic field perpendicular to the area. But it is not so in case of a closed surface. The sum of magnetic flux is always equal to zero for a closed surface. No matter how small the volume, the magnetic sources are always dipole sources, so that there are as many magnetic field lines coming in (to the South Pole) as out (from the North Pole).

It is vital to master the conceptual questions on magnetic flux and dipole as this topic is a gateway to many other topics. You can grasp the concept of magnetics by askIITians through free online IIT study material.

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