# 22.10 Magnetic force between two parallel conductors

 Page 1 / 2
• Describe the effects of the magnetic force between two conductors.
• Calculate the force between two parallel conductors.

You might expect that there are significant forces between current-carrying wires, since ordinary currents produce significant 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 preceding sections. [link] shows the wires, their currents, the fields they create, and the subsequent forces they exert on one another. 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 given to be

${B}_{1}=\frac{{\mu }_{0}{I}_{1}}{2\mathrm{\pi r}}\text{.}$

This field is uniform along wire 2 and perpendicular to it, and so the force ${F}_{2}$ it exerts on wire 2 is given by $F=\text{IlB}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta$ with $\text{sin}\phantom{\rule{0.25em}{0ex}}\theta =1$ :

${F}_{2}={I}_{2}{\text{lB}}_{1}.$

By Newton’s third law, the forces on the wires are equal in magnitude, and so we just write $F$ for the magnitude of ${F}_{2}$ . (Note that ${F}_{1}=-{F}_{2}$ .) 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 the last equation and rearranging terms gives

$\frac{F}{l}=\frac{{\mu }_{0}{I}_{1}{I}_{2}}{2\mathrm{\pi r}}\text{.}$

$F/l$ 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 plasmas. The force exists whether the currents are in wires or not. In an electric arc, where currents are moving parallel to one another, there is an attraction that squeezes currents into a smaller tube. In large circuit breakers, like 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 operational definition of the ampere is based on the force between current-carrying wires. Note that for parallel wires separated by 1 meter with each carrying 1 ampere, the force per meter is

$\frac{F}{l}=\frac{\left(4\pi ×{\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}T\cdot \text{m/A}\right){\left(1 A\right)}^{2}}{\left(2\pi \right)\left(1 m\right)}=2×{\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}\text{N/m.}$

Calculate the Newton's the weight of a 2.5 Kilogram of melon. What is its weight in pound?
calculate the tension of the cable when a buoy with 0.5m and mass of 20kg
what is displacement
it's the time rate of change of distance
Mollamin
distance in a given direction is diplacement
Musa
Distance in a spacified direction
you shouldn't say distance,displacement and distance are two different things .distance can be lopped curved but displacement is always in a straight line so you can't use distance to define it. displacement is the change of position in a specified direction.
Joshua
Well stayed josh👍
Joshua
well explained
Mary
what is the meaning of physics
to study objects in motion and how they interact or take part in the natural phenomenon of the universe.
Phill
an object that has a small mass and an object has a large mase have the same momentum which has high kinetic energy
The with smaller mass
how
Faith
Since you said they have the same momentum.. So meaning that there is more like an inverse proportionality in the quantities used to find the momentum. We are told that the the is a larger mass and a smaller mass., so we can conclude that the smaller mass had higher velocity as compared to other one
Mathamaticaly correct
Mathmaticaly correct :)
I have proven it by using my own values
Larger mass=4g Smaller mass=2g Momentum of both=8 Meaning V for L =2 and V for S=4 Now find there kinetic energies using the data presented
grateful soul...thanks alot
Faith
Welcome
2 stones are thrown vertically upward from the ground, one with 3 times the initial speed of the other. If the faster stone takes 10 s to return to the ground, how long will it take the slower stone to return? If the slower stone reaches a maximum height of H, how high will the faster stone go
30s
how can i calculate it's height
Julliene
is speed the same as velocity
no
Nebil
in a question i ought to find the momentum but was given just mass and speed
Faith
just multiply mass and speed then you have the magnitude of momentem
Nebil
Yes
Consider speed to be velocity
it worked our . . thanks
Faith
Distinguish between semi conductor and extrinsic conductors
Suppose that a grandfather clock is running slowly; that is, the time it takes to complete each cycle is longer than it should be. Should you (@) shorten or (b) lengthen the pendulam to make the clock keep attain the preferred time?
I think you shorten am not sure
Uche
shorten it, since that is practice able using the simple pendulum as experiment
Silvia
it'll always give the results needed no need to adjust the length, it is always measured by the starting time and ending time by the clock
Paul
it's not in relation to other clocks
Paul
wat is d formular for newton's third principle
Silvia
okay
Silvia
shorten the pendulum string because the difference in length affects the time of oscillation.if short , the time taken will be adjusted.but if long ,the time taken will be twice the previous cycle.
discuss under damped
resistance of thermometer in relation to temperature
how
Bernard
that resistance is not measured yet, it may be probably in the next generation of scientists
Paul
Is fundamental quantities under physical quantities?
please I didn't not understand the concept of the physical therapy
physiotherapy - it's a practice of exercising for healthy living.
Paul
what chapter is this?
Anderson
this is not in this book, it's from other experiences.
Paul
am new in the group
Daniel
Sure
What is Boyce law
Boyles law states that the volume of a fixed amount of gas is inversely proportional to pressure acting on that given gas if the temperature remains constant which is: V<k/p or V=k(1/p)