1.1       Magnetic dipole

(a)       The structures, which tend to align along the direction of magnetic field, are known as magnetic dipoles.

(b)       Bar magnet, current carrying solenoid, current carrying coil, current carrying coil, current loop, magnetic needle etc. are the examples of magnetic dipole.

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

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

            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.

1.2       Magnetic flux

(a)       The number of lines of force passing through a given area is defined as magnetic flux.

(b)       The magnetic flux passing through unit normal area is defined as magnetic induction (B).

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

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

(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

(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

            In both cases q is the angle between  .

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

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

(v)        When are antiparallel, then θ = 180^o 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.

(i)         When the plane of coil is parallel to  then θ = 0^o 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 = 180^o, then Φ = 0.

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

            where d A = area of small element.

            = unit normal vector.

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

(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.

            or