A horizontal wire is hung from the ceiling of a room by two massless strings. Th

Question

A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.18 m and a mass of 0.009 kg. A uniform magnetic field of magnitude 0.075 T is directed from the ceiling to the floor. When a current of I = 30 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle ? with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings.

A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.18 m and a mass of 0.009 kg. A uniform magnetic field of magnitude 0.075 T is directed from the ceiling to the floor. When a current of I = 30 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle ? with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings.

Explanation / Answer

For the sum of the forces in the x direction, we have the x component of the tensions and the magnetic force.

We have F = BIL = 2Tsin(angle)

In the y direction, the weight is balanced by the y component of the two tensions...

We have F = mg = 2Tcos (angle)

Starting with the y direction, solve for T

T = mg/2cos(angle) and sub that in for the x direction and get

BIL = mgtan(angle)

(.075)(30)(.18) = (.009)(9.8)(tan (angle))

angle = 77.7 degrees

Then, T = mg/2cos (angle)

T = (.009)(9.8)/(2)(cos 77.7)

T = .207 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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