The drawing shows two long, straight wires that are suspended from a ceiling. Th

Question

The drawing shows two long, straight wires that are suspended from a ceiling. The mass per unit length of each wire is 0.055 kg/m. Each of the four strings suspending the wires has a length of 1.2 m. When the wires carry identical currents in opposite directions, the angle between the strings holding the two wires is 15 degree. What is the current in each wire? Number Units the tolerance is +/-2% By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor.

Explanation / Answer

Force acting on conductor in magnetic field:
F = B I L ..........(1)

Magnetic field near straight wire carrying current I
B = uo I / (2*pi*d) ..........(2)  

When there are two parallel wires on distance d carrying currents I1 and I2, each of them produce magnetic field causing forces acting on wires.
Magnetic field from second wire creates force on first wire:
F1 = B2 * I1 * L
Magnetic field from first wire creates force on second wire:
F2 = B1 * I2 * L
These forces are equal in magnitude:
F = uo I1 I2 L / (2*pi*d) ..........(3)
When currents flow in same direction forces are attractive, and for opposite direction forces are repulsive.
When I1=I2,
F = uo I^2 L / (2*pi*d) ..........(4)

Each wire, suspended on strings, decline from vertical position for angle Q=15°/2 = 7.5°, so that the angle between the strings holding the two wires is 2Q=15°.
We find F from condition of static equilibrium of torques (relative to point where strings are attached to ceiling):
F L cos Q = G L sin ..........(5)
where
G is weight of wire; G = m'gL where m' is the mass per unit of length of each wire.
L is length of strings
from (5) we get relation
F = G tan Q ..........(6)
or
F = m' g L tan Q ..........(7)
and from (4) and (7) :
uo I^2 L / (2*pi*d) = m' g L tan Q ..........(8)  
I = sqrt(2 pi d m' g tan Q / uo) ..........(9)  
d = 2L sinQ ..........(10)
and finally
I = 2 sqrt(pi L m' g sinQ tan Q / uo) ..........(11)
I = sqrt[1.2 * 0.055 * 9.81 * sin 7.5° * tan 7.5° / 10^-7 ]
I = 333.56 A

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.