30. To wires having currents in same directionas shown in figure, attract to each other.Both parallel wires produce magnetic fieldin upward and downward direction to eachother therefore direction of forceon each conductor per unitlength is in opposite directionand along same line of action.hence they attract to each other.Since, electric currents in bothwires is flowing due to movement of treeelectrons in the wires. Explain the givenstatement on the basis of free electronmodel.
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Answer:
You might expect that two current-carrying wires generate significant forces between them, since ordinary currents produce magnetic fields and these fields exert significant forces on ordinary currents. But you might not expect that the force between wires is used to define the ampere. It might also surprise you to learn that this force has something to do with why large circuit breakers burn up when they attempt to interrupt large currents.
The force between two long, straight, and parallel conductors separated by a distance r can be found by applying what we have developed in the preceding sections. (Figure) shows the wires, their currents, the field created by one wire, and the consequent force the other wire experiences from the created field. Let us consider the field produced by wire 1 and the force it exerts on wire 2 (call the force {F}_{2}). The field due to {I}_{1} at a distance r is
{B}_{1}=\frac{{\mu }_{0}{I}_{1}}{2\pi r}
(a) The magnetic field produced by a long straight conductor is perpendicular to a parallel conductor, as indicated by right-hand rule (RHR)-2. (b) A view from above of the two wires shown in (a), with one magnetic field line shown for wire 1. RHR-1 shows that the force between the parallel conductors is attractive when the currents are in the same direction. A similar analysis shows that the force is repulsive between currents in opposite directions.This field is uniform from the wire 1 and perpendicular to it, so the force {F}_{2} it exerts on a length l of wire 2 is given by F=IlB\mathrm{sin}\phantom{\rule{0.1em}{0ex}}\theta with \mathrm{sin}\phantom{\rule{0.1em}{0ex}}\theta =1\text{:}
{F}_{2}={I}_{2}l{B}_{1}.
The forces on the wires are equal in magnitude, so we just write F for the magnitude of {F}_{2}. (Note that {\stackrel{\to }{F}}_{1}=-{\stackrel{\to }{F}}_{2}.) Since the wires are very long, it is convenient to think in terms of F/l, the force per unit length. Substituting the expression for {B}_{1} into (Figure) and rearranging terms gives
\frac{F}{l}=\frac{{\mu }_{0}{I}_{1}{I}_{2}}{2\pi r}.
The ratio F/l is the force per unit length between two parallel currents {I}_{1} and {I}_{2} separated by a distance r. The force is attractive if the currents are in the same direction and repulsive if they are in opposite directions.
This force is responsible for the pinch effect in electric arcs and other plasmas. The force exists whether the currents are in wires or not. It is only apparent if the overall charge density is zero; otherwise, the Coulomb repulsion overwhelms the magnetic attraction. In an electric arc, where charges are moving parallel to one another, an attractive force squeezes currents into a smaller tube. In large circuit breakers, such as those used in neighborhood power distribution systems, the pinch effect can concentrate an arc between plates of a switch trying to break a large current, burn holes, and even ignite the equipment. Another example of the pinch effect is found in the solar plasma, where jets of ionized material, such as solar flares, are shaped by magnetic forces.
The definition of the ampere is based on the force between current-carrying wires. Note that for long, parallel wires separated by 1 meter with each carrying 1 ampere, the force per meter is
\frac{F}{l}=\frac{\left(4\pi \phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−7}}\text{T}\cdot \text{m/A}\right){\left(1\phantom{\rule{0.2em}{0ex}}\text{A}\right)}^{2}}{\left(2\pi \right)\left(\text{1 m}\right)}=2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−7}}\phantom{\rule{0.2em}{0ex}}\text{N/m}.
Since {\mu }_{0} is exactly 4\pi \phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−7}}\phantom{\rule{0.2em}{0ex}}\text{T}\cdot \text{m/A} by definition, and because \text{1 T}=1\phantom{\rule{0.2em}{0ex}}\text{N/}\left(\text{A}\cdot \text{m}\right), the force per meter is exactly 2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{−7}}\phantom{\rule{0.2em}{0ex}}\text{N/m}. This is the basis of the definition of the ampere.
Infinite-length wires are impractical, so in practice, a current balance is constructed with coils of wire separated by a few centimeters. Force is measured to determine current. This also provides us with a method for measuring the coulomb. We measure the charge that flows for a current of one ampere in one second. That is, \text{1 C}=\text{1 A}\cdot \text{s}. For both the ampere and the coulomb, the method of measuring force between conductors is the most accurate in practice.