Electric Dipole

The electric dipole is a pair of opposite and equal point charges, p and -p separated by a distance ‘d’. The centre of the dipole is the midpoint between the p and- p.

• The charges in an electric dipole will be zero as it is a pair of opposite and equal payments.
• Since the charges are separated by some distance thus, the electric field does not cancel out.
• Dipole moment is defined as the product of the magnitude of the charges and the separation of the ends of the dipole.
• Dipole Moment = q x 2d.

Electric Dipole’s Electric Field

Electric dipole’s electric field in space at any point can easily be found out from the superstitious principle and Coulomb’s law. The two cases of results are as follows:

1. At a point on the axis of an electric dipole.
2. When it is on the perpendicular or equatorial plane of the dipole.

Point Dipole: when the 2a approaches the 0.

The dipole field at a point is contrarily balanced to the cube of the distance from the centre to the end.

Physical Significance of Dipole

• The Electric Dipole’s concept is important in physics and has an essential idea in Chemistry.
• Polar Molecules: If the centre of mass of -ve charge doesn’t overlap with the centre of mass of +ve charge, For Example-H2O, Water Molecule.
• Non-polar Molecule: If the centre of mass of -ve charge coincides with the centre of mass of +ve charge, For Example-Carbon, Dioxide.
• The study of electric dipoles is most significant. If the net amount is zero, that doesn’t mean that there will be no electric field or the absence of an electric field, which is evident by studying the electric dipole moment.
• The study of electric dipoles and the Dipole moment helps us to understand the concept of polarisation.
• Polar molecules consist of permanent Dipole moments that are randomly oriented without an external electric field. Still, when the electric field is applied, these polar molecules will align themselves in the electric field direction.

Dipole in a Uniform External Field

The torque on the dipole results from the forces acting at different points irrespective of separated dipoles by some distance. The torque of a dipole is independent of the origin when there is zero net energy. When the toque attempts to align with the electric field, once it gets aligned, Torque becomes 0.

If p is parallel to E or antiparallel to E, the Torque is zero in both cases, but there will be a net force on the Dipole if E is not uniform.

• When p is parallel to E, the net force of the dipole is in the increasing field direction.
• When p is antiparallel to E, the net force of the dipole is in the decreasing field direction.
• in a non-uniform electric field, electric dipole experiences force and torque
• The magnitude of torque: qE x 2a sinӨ = 2qaE sinӨ = pEsinӨ

Continuous Charge Distribution

When charges are continuously spread over a surface, Line, or volume, this distribution is known as continuous charge distribution. Charge density represents how crowded are charged at a specific point.

Gauss’s Law

• The sum of the electric flux out of a closed surface equals the charge encircled by the permittivity as stated by Gauss’s Law.
• The total electric flux through the closed surface is zero, when there is no charge inside the enclosed volume of that closed surface.
• It holds for any secured surface regardless of its shape and size.
• This law helps estimate the electrostatic field for the asymmetric system.
• This Law is based on the Inverse Square dependence on distance in Coulomb’s Law.
• The breach of Gauss’s Law will indicate the withdrawal from the Inverse Square Law.
• The q term on the right-hand side of Gauss’s Law comprises the total of all charges encircled by the plane. These charges may be found anywhere inside the plane.
• The Gaussian surface is the plane we select for applying Gauss’s Law.

Application of Gauss’s Law

The electric field due to a general charge distribution is as follows:

1. Electric field because of a uniformly charged thin spherical shell.
2. Electric field because of uniformly charged infinitely plane sheets.
3. Electric field because of infinitely long straight uniformly charged wire.

Conclusion

An electric dipole is a couple of equal and opposite charges segregated by a short length. Dipole moment has magnitude 2qa, and it is in the direction of the axis from -q to q. According to Gauss’s Law, the total electric flux out of a closed surface is equal to the charge encircled by the permittivity. This Law helps to deduce the electric field. The electric area at a point at a distance r from an electric dipole is proportional to 1/r3.