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Q.37

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

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

The current is .

See the step by step solution

Step by Step Solution

Step 1: Given Information

We need to find current the upper wire to “float” so as to form an equilateral triangle with the lower wires.

Step  2: 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 as:

The weight per unit length is

The forces between the wires on the table and the floating wire are repulsive and act at away from the vertical. From the figure, we see that the horizontal components cancel out and that their vertical components add up. since they have the same magnitude of

The magnitude of the net force which points vertically upwards is simply twice the vertical component of , say,

Step 3: Calculation

Since we are looking at force per unit length we have :

Equating this with weight per unit length we have :

The current is then

Step 4: Figure

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