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Electric dipole is the combination of two charges of equal magnitude but opposite nature separated by small distance.Electric intensity is the force experienced by a unit positive charge placed in the electric field of dipole. Torque is the turning experience got by a electric dipole when placed in an external electric field.

Electric Field intensity on the axial line of dipole

A line passing through two charges is called axial line. We would like to measure the electric field intensity at any point on the axial line of electric dipole. Let us consider a point on the axial line at a distance r from the center of the dipole. We shall imagine a unit positive charge at the considered point. It experience force both due to positive and negative charge. Due to Positive charge force is repulsive and due to negative charge it is attractive. Using Coulomb's inverse square law, we need to write equations for the force experienced by unit positive charge at the given location.We need to measure the effective force as the difference between the two charges and it can be further simplified as shown in the video lesson below. Electric dipole moment is the product of any one charge of the dipole to the distance between the two charges of dipole. It is a vector quantity and its direction is from negative charge towards positive charge. Intensity is expressed in terms of dipole moment as shown below.

Electric field intensity on equatorial line of Dipole

Equatorial line is a line passing through the center of dipole and perpendicular to the axial line. Let us consider a point on that line that is at a finite distance from center of dipole. We shall imagine a unit positive charge at that point and it experience force due to both positive and negative charge of the dipole. Its magnitude can be determined using inverse square law and its value is shown in the video below. The force due to positive charge is repulsive on unit positive charge and force due to negative charge is attractive. Their directions were identified and the resultant is determined using the vector laws of addition as shown in the video lesson below. It can be noticed that the electric intensity on the equatorial line is half that of intensity on the axial line. A detailed proof is given in the video lesson below. Its direction is also shown.

Electric Intensity at any point on the dipole

Let us consider a point around the dipole that is neither on the axial line or equatorial line and the point is at a distance and is making some angle with the horizontal line. To find the electric field intensity at that point, we can consider the dipole as the combination of two dipoles that are perpendicular to each other as shown in the video lesson. For one dipole the considered point is on the axial line and for the other imagined dipole the point is on the equatorial line. As we have derived the equations for the intensity on axial line and equatorial line, we can use that equations and they two are perpendicular to each other. By simplifying them further as shown in the video lesson, we can get the resultant equation as shown. This is a generic equation and in that equation, if the angle is zero, the point will be on axial line and if the angle is ninety degree, the point goes to equatorial line.

Torque experienced by dipole when placed in a uniform electric field

Let us consider a dipole of two charges separated by a small distance and let us apply a electric field of known intensity on it. Each charge experience a force and and the two forces are equal in magnitude but opposite in direction. But they don't cancel each other as the two forces are acting on different points of the electric dipole. Thus it experience a turning effect in anti clock wise direction and we can measure the torque as shown in the video lesson below. Torque is defined as the product of any one force and the perpendicular distance between the two forces acting on the dipole. It is a vector and we can find the direction using the right hand thumb rule or cork screw rule as shown in the video lesson below.