A rectangular loop of wire, L = 26.2 cm and W = 15.4 cm, carries a I1 = 1.83 A current and lies in a plane (d = 13.6 cm), which also contains a very long straight wire carrying a I2 = 10.5 A current.

I used this equation:
F1+F2 = mu0*I1*I2*0.262/(2pi)*(1/0.136-1/0.290)=2.57*10^-7 but this is wrong. Anyone know where I went wrong ?

You have a mistake in the calculations. My result is 3.93•10^-6 N

To understand where you might have made an error, let's break down the problem and the equation you've used.

Firstly, the equation you used is for the force between two parallel conductors due to their magnetic fields. However, in this scenario, we are dealing with a loop of wire and a straight wire. Hence, the force equation you used is not applicable to this situation.

To find the force between the loop and the straight wire, you need to use the equation for the magnetic field produced by a long straight wire at a distance from it, multiplied by the current flowing through the loop.

The equation for the magnetic field produced by a long straight wire at a distance is given by:

B = (mu0 * I2) / (2 * pi * r)

where B is the magnetic field, mu0 is the permeability of free space (equal to 4 * pi * 10^-7 Tm/A), I2 is the current flowing through the straight wire, and r is the distance from the wire.

For a rectangular loop, the force can be calculated by multiplying the magnetic field by the product of the length of the wire segment (L) and the width of the wire segment (W) through which the current flows.

So, the correct equation to calculate the force between the loop and the straight wire would be:

F = (mu0 * I1 * I2 * L * W) / r

Now let's substitute the given values into the formula:

mu0 = 4 * pi * 10^-7 Tm/A
I1 = 1.83 A
I2 = 10.5 A
L = 26.2 cm = 0.262 m
W = 15.4 cm = 0.154 m
r = 13.6 cm = 0.136 m

F = (4 * pi * 10^-7 Tm/A) * (1.83 A) * (10.5 A) * (0.262 m) * (0.154 m) / (0.136 m)

Simplifying the calculation will give you the correct value for the force between the loop and the straight wire.