# Magnetic force on coil problem

• meteorologist1
After integrating this over the coil, you should be able to get the desired result. In summary, the problem involves a long thin coil and a large circular ring, both carrying currents. The goal is to find the force on the coil as a function of its displacement from the center of the ring. To solve this, you can use the formula F=\int I(dl\times B) and integrate over the coil to get the desired result.
meteorologist1
I'm stuck on the following problem:

A long thin coil of length l, cross-sectional area S, and n turns per unit length carries a current I. It is placed along the axis of a large circular ring of radius a, which is carrying a current I'. If d is the displacement of the center of the coil from the center of the ring along the coil axis, find the force on the coil as a function of d.

I'm not sure what formulas to use, and what I have to integrate to get the following result:
$$F = -\frac{\mu_0 II'nSa^2}{2} ((a^2 + (\frac{l}{2} - d)^2)^\frac{-3}{2} - (a^2 + (\frac{l}{2} + d)^2)^\frac{-3}{2})$$

Thanks.

Hello,first post ever, you could try to use the force from the formula

$F=\int I(dl\times B)$

Where B is the field from the ring

Last edited:

## 1. What is the magnetic force on a coil?

The magnetic force on a coil is the force exerted on the coil due to the interaction between the magnetic field and the electric current flowing through the coil. It is perpendicular to both the direction of the magnetic field and the direction of the current.

## 2. How do you calculate the magnetic force on a coil?

The magnetic force on a coil can be calculated using the formula F = BILsinθ, where B is the magnetic field strength, I is the current flowing through the coil, L is the length of the coil, and θ is the angle between the magnetic field and the direction of the current.

## 3. What factors affect the magnetic force on a coil?

The magnetic force on a coil is affected by the strength of the magnetic field, the current flowing through the coil, the length of the coil, and the angle between the magnetic field and the direction of the current. Additionally, the number of turns in the coil and the material of the coil can also affect the magnetic force.

## 4. How does the direction of the current affect the magnetic force on a coil?

The direction of the current affects the direction of the magnetic force on a coil. If the current is flowing in the same direction as the magnetic field, the force will be attractive. If the current is flowing in the opposite direction, the force will be repulsive. If the current is perpendicular to the magnetic field, there will be no force.

## 5. Can the magnetic force on a coil be increased?

Yes, the magnetic force on a coil can be increased by increasing the current flowing through the coil, increasing the number of turns in the coil, or increasing the strength of the magnetic field. Additionally, using a ferromagnetic material for the coil can also increase the magnetic force.

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