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FIGURE EX29.37 is a cross-section through three long wires with a linear mass density 50g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0cmapart and are attached to a table. What current I will allow the upper wire to 鈥渇loat鈥 so as to form an equilateral triangle with the lower wires?

Short Answer

Expert verified

240Acurrent allow the upper wire to 鈥渇loat鈥 so as to form an equilateral triangle with the lower wires.

Step by step solution

01

Given Information

We have given three long wires with a linear mass density 50g/mand the lower two wires 4.0cmare apart and are attached to a table.

02

Simplify

The weight per unit length of the floating wire must be balanced by force per unit length due to the interaction of the current of the floating wire with the other two wires. Set

m=ml=50g/m.

Then weight per unit length is

fg=Fgl=mgl=mg.

The forces between the wires on the table and the floating wire are repulsive and act at

30away from the vertical. From the figure, we see that their horizontal components out and that their vertical components add up. Since they have the same magnitude of

F1=F2=02I2ld,

03

Calculation

The magnitude of the force which points vertically up is simply twice the vertical component of ,say,F1:

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