Equation for Electric Dipole in Uniform Electric Field

The pattern of iron filings represents the magnetic field lines produced by a magnet. However, to quantify the magnetic field precisely, a miniature compass needle with a known magnetic moment, which is m, and inertia moment to oscillate in a magnetic field can be used. 

An electric charge flow around a loop is similar to a magnetic dipole, often a small magnet with atomic or subatomic size. 

Let us learn all about the Equation for Electric Dipole in a Uniform Electric Field in more detail!

Torque

The force applied on the axis determines the direction of torque, which is considered to be a vector type quantity. The magnitude of the torque vector is calculated as given below:

τ = F r sinθ

Here, F represents the force operating on the axis, r represents the moment arm’s length, θ represents the angle formed between the force vector and the moment arm, and τ represents the torque vector.

Electric dipole

An electric dipole moment is the product of the magnitude of the opposite charges of a dipole and the distance between these charges. An electric dipole moment is considered to be a vector since it has a magnitude and a distinct direction of movement from the negative charge towards the positive charge. 

The dipole moment of an electric dipole is given as below, 

p = q d 

Here, q refers to the charge magnitude, and d refers to the separation distance.

Torque on an Electric Dipole in Uniform Electric Field

Let us place a dipole in an external field ‘E’, which is uniform, to estimate the torque that the dipole experiences. The positive charge of the dipole gets subjected to an electric force in the upward direction of magnitude ‘qE’, whereas the negative charge of the dipole gets subjected to an electric force in the downward direction of magnitude ‘qE’.

The dipole may be in translational equilibrium since the total net force becomes zero. What, on the other hand, is rotational equilibrium? Even though the dipole remains stationary in this case, it shows rotation with a specific angular velocity. 

This phenomenon has been proven experimentally, indicating that the behaviour of both the electrostatic forces (qE) is as a clockwise torque. 

Therefore, the dipole shows rotation when placed in an external electric field of uniform nature. Usually, torque is always applied in pairs. Its resultant magnitude is the resultant product of its force and arm. The distance between the place where the force gets applied and the point where the dipole gets rotated can be considered the arm.

Magnetic dipoles include compass needles, bar magnets, and other objects. A current loop’s behaviour will be compared to a magnetic dipole. An atom of a magnetic substance behaves like a dipole because electrons revolve around the nucleus. A magnetic dipole (or magnet’s) north and south poles are always of equal strength and opposite kinds. Furthermore, this type of magnetic pole is always in pairs that can’t be separated. The distance between a bar magnet’s two poles determines its magnetic length.

Magnetic Dipole Moment = Strength of either pole * Magnetic length

                                      M= m(2l)

Uniform Field Torque on a Magnetic Dipole

When a magnetic rod (considered a magnetic dipole) is kept in a uniform magnetic field, the north pole detects a force equal to the multiplication of its magnetic field intensity and the pole strength in the magnetic field direction. 

Despite this, the south pole senses a force of similar magnitude but opposite direction. A torque is imparted to the magnetic dipole that forces it to rotate. 

Conclusion 

In this article, we studied the behaviour of forces acting on a dipole in a uniform magnetic field, torque on an electric dipole in a uniform electric field, and the equation for electric dipole in a uniform electric field that relates to when a dipole is kept in an electrostatic field. We’ve found that if we keep the iron filings near a bar magnet on a piece of paper and pound the sheet, the fillings will assemble themselves in a certain design. The arrangement of iron filings represents the magnetic field lines produced by the magnet. These lines produced by the magnetic field give us a very good indication of the magnetic field.