When the angle between the dipole moment and electric field is 180° then the potential energy of electric dipole is maximum. (II). When the angle between the dipole moment and electric field is zero then the potential energy of electric dipole is minimum.

P.E=−pEcosθ=−p⋅E. This is negative when θ is acute and positive when θ is obtuse.

Potential energy is maximum when dipole moment is anti parallel the the direction of EF ( condition is called unstable equilibrium ) and minimum when dipole moment is parallel to the EF ( Stable Equilibrium ) .

The potential at a point due to an electric dipole will be maximum and minimum when the angles between the axis of the dipole and the line joining the point to the dipole are respectively. V=pcosθr2. If θ=0∘ then Va=max. If θ=180∘ then Ve=min.

Thus, potential energy is minimum when dipole is parallel to B.

Potential Energy of magnetic dipole in a magnetic field is defined as the amount of work done in rotating the dipole from zero potential energy position to any desired position.

Items with high magnetic potential energy, such as metal spoons or ball bearings, respond strongly to a magnetic force. Objects with lower magnetic potential energy, such as a plastic spoon or a rubber ball, are not as affected by a magnetic pull.

When a magnetic rod, (which can be taken as a magnetic dipole), is kept in a uniform magnetic field, the North Pole senses a force equal to the multiplication of the magnetic field intensity and the pole strength in the magnetic field direction.

We can infer from the above two results, the potential energy of the bar magnet is minimum when it is aligned along the external magnetic field and maximum when the bar magnet is aligned anti-parallel to external magnetic field.

Solution : P.E. is minimum, when θ=0∘, i.e., dipole is aligned along the field. =-MB→minimum.

What should be the orientation of a magnetic dipole in a uniform magnetic field so that its potential energy is i) maximum ii) minimum? When the magnetic dipole is aligned along the magnetic field, when θ = 00, it is in stable equilibrium having minimum P.E. which is maximum.

Potential energy of a magnetic dipole in a uniform magnetic field U=−MBcosq clearly the potential energy is maximum when cosθ=−1 or θ=π That is, potential energy is maximum when magnetic dipole with its magnetic moment M is oriented opposite to the direction of magnetic field ( or angle between M and δ is 180o).

What should be the orientation of a magnetic dipole in a uniform magnetic field so that its potential energy is maximum? When the magnetic moment of the magnetic dipole is antiparallel to the magnetic field i.e., when θ = 180°, potential energy is maximum.

Solution: τ = MB sin θ ∴ M = τ/ Bsin θ ∴ M = 0.06/ (0.2 x sin 30°) = 0.06/ (0.2 x 0.5)

5.92

The spin magnetic moment is a magnetic moment caused due to the spin of particles. The formula to find the spin magnetic moment is√n(n+2), where n is the number of unpaired electrons.

The SI unit for magnetic moment is clearly N m T−1. If an electric current I flows in a plane coil of area A (recall that area is a vector quantity – hence the boldface), the torque it will experience in a magnetic field is given by. τ=IA×B. This means that the magnetic moment of the coil is given by.

ampere-meter

Ampere square meter

Pole strength is given by m=M/2l. Unit of magnetic dipole moment is Am2.

: a unit of magnetic pole strength equal to the strength of a magnetic pole that repels an identical pole at a distance of one centimeter with a force of one dyne.

In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted Φ or ΦB. The SI unit of magnetic flux is the weber (Wb; in derived units, volt–seconds), and the CGS unit is the maxwell.

amperes