A dipole is a neutral system with two oppositely charged parts that can affect other charged objects. The dipole moment is a vector quantity describing the strength of this influence. The force exerted by a dipole on a distant particle can be approximated using an equation. Einstein’s theory of relativity relates electric forces to magnetic forces, and a magnetic dipole can be approximated by a dipole of magnetic charges. The dipole moment is useful for determining the force an external field exerts on a dipole, such as in a microwave oven.
A dipole is a neutral system made up of two oppositely charged parts. For example, a water molecule is overall neutral, but one end of it is positively charged while the other is negatively charged. Such an object can affect other charged objects through electromagnetic forces. The dipole moment of a dipole is a vector quantity describing the strength of this influence. Its size is equal to the size of each charge multiplied by the distance between the two parts of the system.
The magnitude of the force exerted by a dipole on a distant particle can be approximated using the equation F=2*pkq/r3. Here, p is the dipole moment, k is Coulomb’s constant, q is the size of the net charge on the far particle, and r is the separation between the center of the dipole and the far particle. This approximation is nearly perfect on the longitudinal axis of the system as long as r is significantly greater than the separation between the two dipole components. For particles far from this axis, the approximation overestimates the force by a factor of 2.
Einstein’s theory of relativity relates electric forces to magnetic forces. The magnetic field of a bar magnet can be approximated by a dipole of magnetic charges, one near the north pole of the magnet, the other near the south pole. Such an assembly is called a magnetic dipole, and the influence it exerts on a distant charge moving perpendicular to the field can be approximated by 2*μqs/r3, where μ is the magnetic dipole moment and s is the velocity.
An electric current moving in a circular wire generates a magnetic field similar to that of a short bar magnet. The magnetic dipole moment of such a wire has magnitude I*A, where I is the current of the wire and A is the area it traces in space. At the atomic level, magnetism is often viewed as arising from the movement of electrons along curved paths. The size of the magnetic dipole moment for such a particle is equal to q*s/(2r), where q is the size of the charge, s is the particle’s velocity, and r is the path radius.
In addition to quantifying the force of a dipole on distant charged particles, the dipole moment is useful for determining the force an external field exerts on a dipole. For example, a microwave oven creates variable electric fields of short duration. These fields cause the water molecules, which are electric dipoles, to rotate. This rotational motion leads to an increase in temperature, which cooks the food. The maximum torque exerted on a dipole by an external field is simply the product of the dipole moment and the field strength.
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