Final answer:
The current (I) in the wires can be found by using Ampère's force law, rearranging it to solve for the current, substituting the given force per unit length, the separation distance, and the permeability of free space, and then performing the calculations to find I in milliamperes.
Step-by-step explanation:
The question involves finding the current (I) flowing through two long, straight, parallel wires that repel each other with a given force per unit length. The force between two parallel conductors carrying currents can be calculated using Ampère's force law, which states that the force per unit length (f) between two parallel currents I1 and I2 separated by a distance r is given by:
f = µ0*I1*I2 / (2π*r)
where µ0 is the permeability of free space. Given that the currents are equal in magnitude and the force per unit length is known, the equation can be rearranged to solve for the current (I).
For two wires repelling each other with a force per unit length of 3.2 nN/m (which is 3.2 x 10^-9 N/m) and separated by a distance of 8.2 cm (which is 8.2 x 10^-2 m), the equation becomes:
I2 = (f * 2 π * r) / µ0
By substituting the given values and solving for I, we find the current in the wires, expressed in milliamperes (mA).
To execute the calculations, we first insert the given values into the rearranged equation:
I2 = (3.2 x 10^-9 N/m * 2 * 3.14159 * 8.2 x 10^-2 m) / (4π x 10^-7 T*m/A)
Then, we compute the value of I2 and take the square root to find the value of I. The result is then converted to milliamperes by multiplying by 10^3.