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Three long, current-carrying wires are parallel to one another and separated by a distance d. The magnitudes and directions of the currents are shown in Figure P30.91. Wires 1 and 3 are fixed, but wire 2 is free to move. Wire 2 is displaced to the right by a small distance x. Determine the net force (per unit length) acting on wire 2 and the angular frequency of the resulting oscillation. Assume the mass per unit length of wire 2 is λ and x ≪ d.
FIGURE P30.91
(a)
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The net force per unit length acting on wire
Answer to Problem 91PQ
The net force (per unit length) acting on wire
Explanation of Solution
The wire
The direction of magnetic field on wire
Write the expression of the force between two parallel current carrying conductors per unit length.
Here,
Substitute
Here,
Substitute
Here,
Write the expression for the net force on wire
Conclusion:
Substitute
Since
This implies that
Thus, the net force (per unit length) acting on wire
(b)
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The angular frequency of the resulting oscillation.
Answer to Problem 91PQ
The angular frequency of the resulting oscillating is
Explanation of Solution
Rewrite the equation (V).
Since, the wire
Write the expression for the force experienced by the wire
Rearrange the above expression.
Here,
Substitute
Rearrange the above expression.
Write the general expression for our oscillating wave.
Here,
Compare equation (VIII) is and (IX) for the coefficient of
Conclusion:
Hence, the angular frequency of the resulting oscillation is
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Chapter 30 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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