Concept explainers
(a)
Find the force per unit length exerted on wire A.
(a)
Answer to Problem 65PQ
The force per unit length exerted on wire A is
Explanation of Solution
The curent flowing in all the wires is in the same direction. Therefore, the wires will be attracted towards each other.
The forces acting on the wire A due to the current in the wire B and wire C are as shown below.
Write the expression for force exerted on wire A due to current in wire C as.
Here,
Write the expression for force exerted on wire A due to current in wire B as.
Here,
The components of the forces
Write the expression for component of the forces along the X-axis as.
Here,
Write the expression for component of the forces along the Y-axis as.
Here,
Write the expression for the net force on the wire A as.
Here,
The distance between all the three wires is same. Therefore the wires form an equilateral triangle. So, the angle between the two forces is
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the force per unit length exerted on wire A is
(b)
Find the force per unit length exerted on wire B.
(b)
Answer to Problem 65PQ
The force per unit length exerted on wire B is
Explanation of Solution
The forces acting on the wire A due to the current in the wire B and wire C are as shown below.
Write the expression for force exerted on wire B due to current in wire A as.
Here,
Write the expression for force exerted on wire B due to current in wire Cas.
Here,
The components of the forces
Write the expression for component of the forces along the X-axis as.
Here,
Write the expression for component of the forces along the Y-axis as.
Here,
Write the expression for the net force on the wire B as.
Here,
The wires form an equilateral triangle. So, the angle between the two forces is
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the force per unit length exerted on wire B is
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Chapter 30 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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