Easy physics problem, finding forumula

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To find the force on each wire, the correct formula is F_BA = I_B * L * B, where B is the magnetic field strength. The user initially misinterpreted the variables and used the wrong lengths for L and D. It’s clarified that L should be L2 and D should be the distance between the wires. The forces on the wires will be equal and opposite, and the external magnetic field must be included in the calculations. Proper substitution of values will yield the correct results.
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I have included a picture.

Question:
What is the force on each wire if B = 1.656T, i = 10A, L1 = 7cm and L2 = 14cm?

Now, I have checked my physics book, and the equation I have found is
F_12 = mu_0*L*I1*I2/(2*pi*D)

where D is the distance between the two wires, and L is the length of one wire.

However, I tried that formula in the computer, and it doesn't work. I let L =L2 (m), D=L1 (m), I have tried I1=10 and I2=+/- 10...but it didn't work.

I'm thinking there is another round about way to do this, but I don't know what. CAn someone lend me a hand?
 

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Hey

Ok, the formula is right, you got all the information right under your nose. You're just interpreting wrong.

We know that the wires, let's denote them A and B, are going to have equal and opposite forces.

The equation is F_BA = I_B*L X(cross) B

F_BA = I_B*L * mu_0*I_A/(2*pi*D)
Ok, well, your B is already given to you, which you can substitute for the mu_0*I_A/(2*pi*D).

Let I_B = current, and your L = L2 and that should do the trick.

Well
 
Did you include the external magnetic field?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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