Dipole Moment

Introduction

For the measurement of the extent of polarity, Pauling introduced the concept of Dipole moment. It is denoted by ‘µ’.

The multiplication of positive or negative charge (q) and the distance (d) between two poles are called dipole moment.

Here

–µ = q × d (magnitude of charge × distance)

Dipole moment is a vector quantity, i.e. it has both magnitude as well as direction.

• The Polarity of any polar covalent bond or molecule is measured in terms of dipole moment
• The Direction of dipole moment is represented by an arrow pointing from electropositive to electronegative element and from central atom to one pair of electrons
• Unit of dipole moment is Debye

1 Debye = 1 × 10-18  e.s.u. cm = 3.33 × 10-30 coulomb metre.

In the diatomic molecule µ depends upon the  difference of EN i.e 

µ ∝ ∆EN

order of µ , H-F > H-Cl > H-Br > H-I 

µ = 0 for H-H, F-F, Cl-Cl, Br-Br, O-O

1. For polyatomic molecules, µ depends upon the vector sum of dipole moments of all the covalent bonds.
2. For PCl5 and SF6,  etc. µ=0 due to their symmetrical geometry ( according to charge).
3. Benzene, naphthalene, diphenyl have µ = 0 due to their planar structure
4. If the vector sum is zero then the compound is said to be a non-polar, articles compound or symmetrical geometry ( and it is not essential that an individual µ of every bond should be zero.)

Example – BX3, CCl4,  SiCl4, CH4, CO2, CS2P, Cl5, SiH4 etc. 

In these examples, the bonds B-F, C-Cl, C-H, C-O, P-Cl etc., are polar even though compounds are non-polar.

• The dipole moment of H2O is 1.85 D which is the resultant µ of two O-H bonds. µ of H2O > µ of H2S because the electronegativity of oxygen is higher than sulphur
• Angular structure of the molecule has a greater dipole moment

Applications of dipole moment

• To determine polarity and geometry of molecule:-

If µ = 0 compound is non-polar and symmetrical.

e.g. CO2, BF3, CCl4, CH4, BeF2 etc.

If µ ≠ 0, the compound will be polar and unsymmetrical.

H2O, SO2, NH3, Cl2O, CH3Cl, CHCl3 etc.

• To calculate % ionic character:-

% ionic character = Experimental value of μ÷theoretical value ofμ ×100

• To distinguish cis form or trans form:-

1. Dipole moment of cis isomer is normally higher than trans isomers. For example;
2. If two groups have opposite inductive effects then the trans – isomer will have greater dipole moment. For example;

• To locate the position of substituents in aromatic compounds

              µ =  1 ÷bond angle

1. If the same substituents are present in the symmetrical position of µ of benzene ring compounds will be zero.
2. As the angle between vectors decreases, the value of µ increases.

Electric dipole:

A system of two equal and opposite charges separated by a small distance is called an electric dipole. Every dipole has a characteristic property called dipole moment. It is defined as the product of magnitude of either charge and the separation between the charges, given as

P = q × d 

In certain molecules, the centres of positive and negative charges do not coincide. This results in the formation of electric dipoles. Atom is nonpolar because the centres of positive and negative charges in it coincide. Polarity can be induced in an atom by the application of electric field, in that case it is called an induced dipole.

Electric dipole moment

Electric dipole moment is given as, 

p = q × d

1. It is a vector quantity directed from negative to positive charge.
2. Dimensions : ( Units:) coulomb × metre (or C-m)
3. Practical unit is “debye” ≡ two equal and opposite point charges each having charge 10-10 franklin (~e) and separated by 1 A⁰ has dipole moment of 1 debye.

1 debye = 10-10 × 10-10 Fr × m = C ×m÷ 3×10-30 = 3.3 × 10-30 C-m

Dipole Placed in uniform Electric Field

Figure shows a dipole of dipole moment p placed at an angle θ to the direction of the electric field. Here the charges constituting the dipole experience forces qE each in opposite directions as shown.

Fnet= qE+-qE=0

Thus we can state that when a dipole is placed in a uniform electric field, net force on the dipole is zero. But as equal and opposite forces act with a separation in their lines of action, they produce a couple which tend to align the dipole along the direction of the electric field. The torque due to this coupe can be given as 

µ=r ×f=d ×qE=qd ×E =p ×E

Magnetic Dipole Moment:

A magnetic dipole moment consists of a pair of magnetic poles of equal and opposite strength separated by a small distance. Ex. Magnetic needle, bar magnet, current carrying solenoid, current carrying coil or loop.

Magnetic moment of Bar magnet :-

The magnetic moment of a bar magnet is defined as a vector quantity having magnitude equal to the product of pole strength (m) with effective length (l) and directed along the axis of the magnet from south pole to north pole.

M= ml 

It is an axial vector

S.I. unit is A-m2

Magnetic moment of current carrying coil (loop):-

Current carrying coil or loop behaves like a magnetic dipole. The face of the coil in which current appears to flow anticlockwise acts as north pole, while the face of the coil in which current appears to flow clockwise acts as south pole.

• A loop of geometrical area ‘A’ carries a current ‘I’ then magnetic moment of coil M = I A
• A coil if turns ‘N’, geometrical area ‘A’, carries a current ‘I’ then magnetic moment M = N I A

Magnetic moment of the current carrying coil is an axial vector M = NIA where A is an area vector perpendicular to the pane of the coil and along its axis.

S.I. unit : A-m2 or J/T

Direction of M is found out by right hand thumb rule

• Curling fingers In the direction of current
• Thumb ⟹ Gives the direction of M

For a current carrying coil, its magnetic moment and magnetic field vectors are parallel axial vectors.

Golden key points:-

• Attractive property : A bar magnet attracts certain magnetic substances (e.g. iron, dust). The attracting power of the bar magnet is maximum at two points near the ends called poles. So the attracting power of the bar magnet at its pole is called ‘pole strength’
• The ‘pole strength’ of the north and south pole of a bar magnet is conventionally represented by +m and -m respectively
• The ‘pole strength’ is a scalar quantity with S.I. unit A-m
• The pole strength of a bar magnet is directly proportional to its area of cross section. m A
• The attracting power of a bar magnet at its centre point is zero, so it is called ‘neutral point’

Conclusion

In this text we discovered about the Dipole moment, electric dipole, magnetic dipole moment, magnetic dipole moment in brief. We also learned about their formulas and their applications.