What is the maximum deflection of a wire at its center?

In summary, the conversation discusses the equation Y = (IBX) / 2T, where Y represents maximum deflection, I is current, B is electric field, and T is temperature. The equation is used to find the maximum deflection in the middle of a wire with length L, with one end at L/2 and the other at -L/2. Substituting x = 0 gives the equation for Ymax, which is equal to (IB) / 2T. There is also a question about differentiating Y with respect to L, which is not the correct approach in finding Ymax.
  • #1
Jenkz
59
0

Homework Statement



Y = (IBX) / 2T

I- current
B-electric field
T- temperature

The maximum deflection will be in the middle of the wire (at x = 0). Let L be the total length of the wire, so that one end is at L/2 and the other at –L/2. Substitute this for x in equation 5 to find the maximum deflection, Ymax. This is the y displacement between the centre and the ends of the wire.

The Attempt at a Solution


To find Ymax, do I different Y by by L? so dY/dL = 0 ?
 
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  • #2
No, you don't differentiate Y with respect to L.To find Ymax, you need to substitute x = 0 in the equation and solve for Y.Y = (IB) / 2T when x = 0,Ymax = (IB) / 2T
 

1. What is the maximum deflection of a wire?

The maximum deflection of a wire refers to the maximum amount that a wire can bend or deform before it reaches its breaking point. It is typically measured in units of length, such as meters or inches.

2. What factors affect the maximum deflection of a wire?

The maximum deflection of a wire is influenced by several factors, including the material of the wire, its thickness, the amount of force applied to it, and the length of the wire. Other factors such as temperature and environmental conditions can also play a role.

3. How is the maximum deflection of a wire calculated?

The maximum deflection of a wire can be calculated using various formulas, depending on the specific characteristics of the wire. In general, it involves considering the wire's physical properties, such as its modulus of elasticity and moment of inertia, and applying equations that relate these properties to the applied load and length of the wire.

4. Why is it important to know the maximum deflection of a wire?

Knowing the maximum deflection of a wire is crucial for ensuring the safety and reliability of structures that use wires, such as bridges, suspension cables, and electrical wiring. It helps engineers determine the appropriate diameter and strength of the wire needed for a specific application, and can also help identify potential failure points.

5. Can the maximum deflection of a wire be altered?

The maximum deflection of a wire can be altered by adjusting various factors, such as the material or thickness of the wire, the way it is supported, and the amount of force applied to it. However, it is important to note that there are limits to how much the deflection can be changed without compromising the structural integrity of the wire.

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