Two parallel straight conductors 5 m long and 12 cm apart are to have equal currents. The force each conductor experiences from the other is not to exceed 2x10^-2 N. What is the maximum possible current in each conductor?
I'm getting a ridiculous answer of 1200 A. I'm doing
2x10^-2=((4pix10^-7)(2I)(5))/(2pi.12)
It was supposed to be I^2 not 2I
To solve this problem, you can use the formula for the force between two parallel conductors carrying current. The formula is given by:
F = (μ0 * I1 * I2 * L) / (2 * π * d)
Where:
F is the force between the conductors,
μ0 is the permeability of free space (4π × 10^(-7) T·m/A),
I1 and I2 are the currents flowing through the conductors,
L is the length of the conductors,
d is the distance between the conductors.
In this case, the force is given to be 2 × 10^(-2) N, the length of the conductors (L) is 5 m, and the distance (d) is 12 cm (or 0.12 m).
Using this information in the formula, we can solve for the maximum current (I1 = I2) that each conductor can carry without exceeding the given force limit.
2 × 10^(-2) N = (4π × 10^(-7) T·m/A) * I^2 * 5 m / (2 * π * 0.12 m)
Let's simplify the equation:
2 × 10^(-2) N = (4π/2π) * (10^(-7) T·m/A) * I^2 * (5 m / 0.12 m)
2 × 10^(-2) N = 2 * 10^(-7) T·m/A * I^2 * 41.67...
Now we can divide both sides by 2 × 10^(-7) T·m/A and then multiply by 41.67... to get rid of the constant:
10 = I^2 * 41.67...
Rearranging the equation to solve for I:
I^2 = 10 / 41.67...
Taking the square root to solve for I:
I ≈ √(10 / 41.67...)
I ≈ 0.451 A
Therefore, the maximum possible current in each conductor is approximately 0.451 A, not 1200 A as you mentioned.