Find the magnitude of force per unit length exerted by one wire on the other

In summary, two parallel wires with a distance of 16 cm between them have currents of 24 A in the negative x direction. Using the equation F/L= Uo*ia*ib/(2*pi*d), where d is the distance between the wires, the magnitude of the force per unit length exerted by one wire on the other can be calculated. By plugging in the values, the correct answer of 1440 μN/m is obtained. However, the distance between the wires should be taken as the magnitude of the difference between the two y values, which is 16 cm, rather than adding them together.
  • #1
mba444
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Homework Statement



Two long straight wires in the xy plane are
parallel to the x axis. One wire is at y =
−8 cm and the other wire is at y = 8 cm. The
current in each wire is 24 A and the currents
are in the negative x direction.
The permeability of free space is 4 π ×
10−7 T · m/A.

Find the magnitude of the force per unit
length exerted by one wire on the other. An-
swer in units of μN/m.

Homework Equations



F/L= Uo*ia*ib/(2*pi*d)

The Attempt at a Solution



what i did is that i assumed that one of the wires is at point zero , so i used the equation aboove plugging in these values
F/L= (4*pi*10^-7*24*24)/(2*pi*.08) = i got 1440
which is wrong !

is there what I am doing wrong or is it just a calculation mistake

need your help !
 
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  • #2
What's the distance between the two wires?
 
  • #3
if i add both the (-8+ 8) i will get zero .. unless i take the magnitude of the of the first so that i get 16

im really not sure =S
 
  • #4
i used the 16 and i got it right .. therefore thanks for your help DOC AL
 
  • #5
One wire is at -8, the other is at +8. How far apart are they?
 

What is the concept of force per unit length?

Force per unit length is a measurement of the amount of force exerted by one object on another, divided by the length of the objects in contact. It is often used to describe the force between two wires or cables.

How is the magnitude of force per unit length calculated?

The magnitude of force per unit length is calculated by dividing the force between two objects by the length of the objects in contact. It is typically measured in units of newtons per meter (N/m).

What factors affect the magnitude of force per unit length?

The magnitude of force per unit length is affected by the strength and distance of the two objects, as well as any external forces acting on the objects.

Why is it important to calculate the magnitude of force per unit length?

Calculating the magnitude of force per unit length is important for understanding the interactions between objects, and for designing and engineering structures that can withstand these forces.

How can the magnitude of force per unit length be measured experimentally?

The magnitude of force per unit length can be measured experimentally using a force sensor or by measuring the deflection of a wire under tension. It can also be calculated using mathematical equations based on the properties of the objects and the forces acting on them.

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