Answered: 6.0 cm Figure P19.72

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Two long, parallel wires, each with a mass per unit length of
0.040 kg/m, are supported in a horizontal plane by 6.0 - cm - long
strings, as shown in Figure P19.72. Each wire carries the same

current I, causing the wires to repel each other so that the
angle θ between the supporting strings is 16°. (a) Are the currents
in the same or opposite directions? (b) Determine the
magnitude of each current.

Expert Solution

Step 1

(a)

Given info: The mass per unit length of the two wires is 0.040 kg - m!.
The length of the string by which the wires are suspended is 6.0 cm. The
magnitude of the current in both the wires is same. The angle between
the suspending string is 16°.
Explanation:
The arrangement of the wires is given by the following figure.
Bc
B,
P.
Bp
Вв
0.200 m
When the current in two parallel wires are in the same direction, the
force is attractive. When currents are in opposite direction the force is
repulsive.
Since the wires are repelling each other, the direction are opposite to
each other.
0.200 m

Step 2

(b)

Since the system of wires is in equilibrium, the net force in y-direction
and the x-direction will be zero.
Net force along the y-direction will be,
F, = T cos 8.0° –- mg
Tis the tension in the strings
• m is the mass of the wires
g is the freefall acceleration
Since the force along y-direction is zero, the tension on the string is,
тg
(1)
T=
Cos 8.0
Net force along x-axis will be,
F, = Fm – T sin 8.0°
Fm is the magnetic force
Net force in the direction of x-axis is also zero, the magnetic force will
be,
T sin 8.0°
(2)
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