# Electric Dipole

Electric Dipole moment is the measure of the polarity of the system. It is the separation of positive charge and a negative charge by a distance. The SI unit of electric dipole moment is Coulomb-meter. The simplest example is a pair electric charge of two opposite sign and equal magnitude separated by distance.

## What is Electric Dipole?

Suppose there are two charges of equal magnitude ‘q’, separated by a distance ‘d’. Let the first charge be negative and the second charge be positive. This combination can be called as an electric dipole. Therefore, we can say that an electric dipole is created by the combination of equal and opposite charges by a separation of a certain distance.

Now, the electric dipole moment for this pair of equal and opposite charges is equal to the magnitude of the charges multiplied by the distance between them.

### Magnitude of Electric Dipole Moment

The magnitude of electric dipole moment can be written as:

 $\overrightarrow{p}$ = $q \overrightarrow {d}$

## Direction of Electric Dipole Moment

The electric dipole moment is a vector quantity; it has a defined direction which is from the negative charge to the positive charge. Though, it is important to remember that this convention of direction is only followed in Physics. In Chemistry, the convention is taken to be opposite i.e. from positive to negative. The line along the direction of an electric dipole is called the axis of the dipole.

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### Electric potential due to a Dipole (V)

Suppose there are two charges –q, placed at A, and +q placed a B, separated by a distance d, forming a dipole. Suppose the midpoint of AB is O.

The Electric potential due to a dipole at any point P, such that OP = r will be:

 V = $\frac{1}{4\pi \epsilon } \frac{p cos \theta }{r^{2}}$

Case 1: If θ = 90°

 Electric potential = V = 0

Case 2: If θ = 0°

 Electric potential = V = $\frac{1}{4\pi \epsilon } \frac{p }{r^{2}}$

### Electric Dipole Questions

Q1) Define electric dipole.

An electric dipole is the measure of a system’s overall polarity. It is defined as the measure of positive and negative electrical charges within a system.

Q2) Which of the following is true of an electric dipole.

1. A pair of equal and unlike charges separated by a small distance
2. A pair of unequal and like charges located at the origin
3. A pair of equal and like charges located at the origin
4. A pair of unequal and unlike charges separated by a small distance

Answer: a. A pair of equal and unlike charges separated by a small distance

An electric dipole is a pair of equal and unlike charges separated by a small distance.

Q3) Find the potential due to the dipole when the angle subtended by the two charges at the point P is perpendicular.

Answer: The potential due to the dipole when the angle subtended by the two charges at the point P is perpendicular is zero.

The potential due to a dipole is given by the formula V = m cos θ/(4πεr2). When the angle is perpendicular θ = 90, therefore cos 90 = 0 as result of which the potential is zero.

Q4) Dipole moments are used to calculate the _____.

1. susceptibility
2. electric field intensity
3. strength of the dipole in the field
4. polarisation patterns

Dipole moments are used to calculate the polarisation pattern.

Q5) Calculate the distance between two charges of 6 C with a dipole moment of 8 units.

The dipole moment of a pair of charges is given by the formula

M = Q x d

Rearranging the formula, we get

d = M/Q

Substituting the values in the above equation, we get

d = 8/6 = 1.33 units

Q6) Calculate the dipole moment of equal charges of 7C separated by a distance of 4 cm.

The dipole moment of charge can be calculated as follows:

M = Q x d

Substituting the values, we get

M = 7 x 0.04 = 0.28 C-m

The dipole moment of the given pair of charge is 0.28 C-m.

Q7) Dipole under the influence of an electric field will undergo _____.

1. Polarisation
2. Electromagnetism
3. Magnetisation
4. Magnetism

Dipole under the influence of an electric field will undergo polarisation.

Q8) The electric potential due to a dipole is given by the formula _____.

$V=\frac{1}{4\pi \varepsilon }\frac{p\cos \Theta}{r^2}$

The electric potential due to a dipole is given by the formula $V=\frac{1}{4\pi \varepsilon }\frac{p\cos \Theta}{r^2}$.

Q9: What is the net force acting on a dipole placed in a uniform electric field?

Ans: The forces on the two charges constituting dipole are equal and opposite. Hence the net force is zero.

Q10: What is the SI unit of dipole moment?

Ans: The SI unit of dipole moment is Coulomb.meter

Q11: Define the dipole axis of a dipole.

Ans: The line passing through the two opposite charges of a dipole is called dipole axis

Q12: Define the equatorial axis of a dipole?

Ans: The line passing through the centre of the dipole axis and perpendicular to the dipole axis is called the equatorial axis.

Q13: When is the torque on a dipole is maximum?

Ans: When the axis of the dipole is perpendicular to the field.

Q14: When is the torque on a dipole is minimum?

Ans: When the axis of the dipole is parallel to the field.

Q15: When an electric dipole is in stable equilibrium in an electric field?

Ans: When dipole moment is parallel to the electric field.

Q16: What is the electric dipole moment?

Ans:  It is the measure of the strength of electric dipole. Its magnitude is equal to the product of the magnitude of any one charge and the distance between them.

Q17: Give an example for the electric dipole.

Ans: A pair electric charge of two opposite sign and equal magnitude separated by a distance.

Q18: Give the expression for the magnitude of an electric dipole.

Ans: p = 2qa

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#### Practise This Question

A coil of 100 turns of dimensions 25cm×4cm carries a current of 2A. It makes an angle of 37 with a Magnetic field of 10T. Find the torque acting on it. Also find the work done to rotate it such that the angle increases to 53.