A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.11 m and a mass of 0.010 kg. A uniform magnetic field of magnitude 0.055 T is directed from the ceiling to the floor. When a current of I = 29 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle φ with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings.

Question

Physics

Serenity Rasmussen

24 March, 06:11

A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.11 m and a mass of 0.010 kg. A uniform magnetic field of magnitude 0.055 T is directed from the ceiling to the floor. When a current of I = 29 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle φ with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings.

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Answers (1)

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Cali Avila · Answer 1

The magnetic force acting horizontally will deflect the wire by angle φ from the vertical

Let T be the tension

T cosφ = mg

Tsinφ = Magnetic force

Tsinφ = BiL, where B is magnetic field, i is current and L is length of wire

Dividing

Tanφ = BiL / mg

=.055 x 29 x. 11 /.010 x 9.8

= 1.79

φ = 61°.

Tension T = mg / cosφ

=.01 x 9.8 / cos61

=.2 N.