A long horizontal wire carries a current of I 1 = 22.5 A. A second wire, made of

Question

A long horizontal wire carries a current of I1 = 22.5 A. A second wire, made of 0.400 mm diameter copper wire, is 64.0 cm below the first wire and is held in suspension magnetically. What is the magnitude and direction of the current in the bottom wire? Give a + sign if I2 is parallel to I1, and a - sign if I2 is opposite to I1.
The mass density of Copper is 8.93

A long horizontal wire carries a current of I1 = 22.5 A. A second wire, made of 0.400 mm diameter copper wire, is 64.0 cm below the first wire and is held in suspension magnetically. What is the magnitude and direction of the current in the bottom wire? Give a + sign if I2 is parallel to I1, and a - sign if I2 is opposite to I1. The mass density of Copper is 8.93?103 kg/m3.

Explanation / Answer

The magnetic force is the same as the mass here so they cancel,

B I2 L = m g

--> I2 = m g / [B L]

As B = uo I / [2 pi d]

I2 = [2 pi m g d] / [uo I L]

or

I2 = [2 pi (m/L) g d] / [uo I]

As m/L = D A = 1.122E-3 kg/m.

Thus,

I2 = 1564 A [ANSWER]

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