# Need help on torques / magnetic fields

• vaxopy
In summary, the problem involves finding the ratio of maximum torques experienced by a square coil and a rectangular coil, made from the same length of wire and containing a single turn, in the same magnetic field when they have the same current. By using the fact that the perimeters of the two shapes are equal, the sides of the rectangle can be expressed in terms of the square's side length. The ratio of the areas of the two shapes is then calculated, resulting in the final ratio of 1/2.
vaxopy
A square coil and a rectangular coil are each made from the same length of wire. Each contains a single turn. The long sides of the rectangle are twice as long as the short sides. Find the ratio tsquare/trectangle of the maximum torques that these coils experience in the same magnetic field when they contain the same current.

Im very confused how to do this :/

Let L be length of the squares sides. Using the fact that the perimeter's are equal you can write the length and width of the rectangle in terms of L.

Remember that torque = u X B where u is the magnetic dipole moment of the loop. Since there is no requirement for the magnitude or direction of B, you can just let B=1 and be perpendicular to u so that u X B = u.

i don't know if i did this right
it seems too easy..
t = torque, s=square, r=rectangle

t = NIABsino (o = theta)
ts/tr = NIAsB/NIArB = As/Ar = L^2/2L^2 = 1/2

is this right?

Your right in that it's just the ratio of the areas, but you don't have the correct area for the rectangle. You know that 2 sides of the rectangle are twice as long as the other sides.

Use a different variable to define the sides of the rectangle then use the fact that the perimeters are the same to find the sides of the reactangle in terms of L.

## 1. What is torque?

Torque is a measure of the force that causes an object to rotate about an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point where the force is applied.

## 2. How is torque related to magnetic fields?

Torque and magnetic fields are related through the Lorentz force, which describes the force on a charged particle moving through a magnetic field. The direction of the torque is perpendicular to both the force and the magnetic field.

## 3. What is the formula for calculating torque on a magnetic dipole?

The formula for calculating torque on a magnetic dipole is T = μ x B, where T is the torque, μ is the magnetic dipole moment, and B is the magnetic field strength.

## 4. How can I use torque to control the motion of a magnet?

By applying a torque to a magnet, you can control its motion and orientation. This can be useful in various applications such as motors and generators.

## 5. What are some real-world applications of torques and magnetic fields?

Torques and magnetic fields have a wide range of applications, such as in electric motors, generators, MRI machines, and particle accelerators. They are also used in everyday objects like speakers, computer hard drives, and magnetic levitation trains.

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