Mass needed to balance the magnetic force on upper rod

In summary, the problem involves two parallel rods carrying opposite currents and finding the mass needed to balance the repulsive magnetic force. The equations used are the magnetic force between parallel wires and the force due to gravity. The calculated answer of 1.98 g was initially marked as incorrect, but has now been corrected by the teacher.
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Homework Statement


Two straight rods 60 cm long and 2.0 mm apart in a current balance carry currents of 18 A each in opposite directions. What mass must be placed on the upper rod to balance the magnetic force of repulsion?

## \mu_0 = 4 \pi * 10^-7 ~\frac {T * M} {A}##
## g = 9.81 ~m/s ##


Homework Equations


Magnetic force between parallel wires: ## ~{dF_{12}} = I_2{d\ell_2} \frac {\mu_0 I_1 } {2\pi R} ##
Force due to gravity: ## ~F = mg ##

The Attempt at a Solution


My initial assumption (and the textbook's method) is to find the magnetic force and set it equal to F = mg. However, I keep getting the magnetic force as being ## \frac {18^2*(.6)*(4 \pi * 10^-7)} {2 \pi *(.002)} ## = .01944 N, and when I set that equal to mg and divide by 9.81 I get a mass of 0.00198 kg = 1.98 g, which is not the correct answer. I know the correct answer is 0.99 g (the problem is multiple choice), but for the life of me I can't seem to figure out how to get to that answer.
 
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  • #2
I don't see anything wrong with your method or answer. It is likely that the answer given in the book is incorrect.
 
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  • #3
I was afraid of that, but I just wanted to make sure I wasn't missing anything obvious. Thank you.

EDIT: My teacher actually just changed the correct answer on the homework to 1.98 g. Wonder if he saw this?
 
Last edited:

1. What is the "magnetic force" on the upper rod?

The magnetic force on the upper rod refers to the force exerted on the rod by a magnetic field. This force is proportional to the strength of the magnetic field and the length of the rod.

2. How is the magnetic force on the upper rod calculated?

The magnetic force on the upper rod can be calculated using the formula F = BIL, where B is the magnetic field strength, I is the current flowing through the rod, and L is the length of the rod. This formula is known as the Lorentz force law.

3. Why is the mass needed to balance the magnetic force on the upper rod?

The mass is needed to balance the magnetic force on the upper rod because the force of gravity acting on the mass creates an equal and opposite force, allowing the rod to remain in equilibrium with the magnetic force.

4. What factors affect the amount of mass needed to balance the magnetic force on the upper rod?

The amount of mass needed to balance the magnetic force on the upper rod depends on several factors including the strength of the magnetic field, the current flowing through the rod, and the length of the rod. Additionally, the force of gravity and the distance between the mass and the rod can also affect the amount of mass needed.

5. How does the mass needed to balance the magnetic force on the upper rod impact experiments or applications?

The mass needed to balance the magnetic force on the upper rod can impact experiments or applications by influencing the behavior of the rod and the accuracy of the results. The amount of mass needed may also vary depending on the specific conditions of the experiment or application, so it is important to carefully consider and control this factor for accurate and reliable results.

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