# What is the Magnetic Force on the Loop in this Rigid Contour System?

• Ivan Antunovic
In summary, the problem involves determining the intensity of magnetic force acting on a wire loop in a plane, given that the loop lies in vacuum and is parallel to a long line cable. The current in the loop is 100 A and the correct answer for the force is F = 386 mN. The conversation also includes discussions about the equations involved and the correct setup for the loop integral. It is noted that the area element and the flux density must be taken into consideration. The conversation also addresses an incorrect solution and the correct solution is given as F = I dFi/ dx.
Ivan Antunovic

## Homework Statement

Rigid contour of an isosceles triangle and a long line cable lie in a plane and are located in vacuum . Determine the intensity of the magnetic force F acting on the loop. Current I = 100 A.

F = 386 mN.
I am getting 2 mN.
Notice that I found dS by splitting while triangle in two triangles.

## The Attempt at a Solution

How is the derivative in the last line not zero?
Does the magnetic flux through the loop change with time?

In the problem description, the wire loop is not carrying a current.
ds is a line element and dS is a surface element... not always clear which you intend.
ie. The area element between x and x+dx, inside the triangle, is dS=2y(x)dx : y=(x-a)/2
So dS=(x-a)dx ... that what you mean?
Then: ##\vec B = \frac{\mu_0 I}{2\pi x}\hat k## and ##d\Phi = \vec B\cdot d\vec S##
... means the flux density $$\Phi = \frac{\mu_0 I}{2\pi}\int_a^{2a}\frac{x-a}{x}\text{d}x$$ ... which is where you ended up.

What about ##\vec F= I\oint (d\vec s\times \vec B)## ?

You mean something like this , still I don't understand how there can be force on the loop if there is no current I flowing through loop.

image sharing

By the way I think I messed something up because a didn't cancle out in F.Guess because I didnt do the loop integral the right way

Last edited:
Please guys help me I am trying to figure out the whole day how my solution is incorrect, in the solution there is mi zero * I^2 / (2*pi) [1/2 - ln2] and I am having 1 - ln2 in the brackers , where did he get that one half from.

## What is magnetic force on a loop?

Magnetic force on a loop is the force exerted on a current-carrying loop placed in a magnetic field. It is the result of the interaction between the magnetic field and the electric current flowing through the loop.

## How is the direction of magnetic force on a loop determined?

The direction of magnetic force on a loop is determined by the right-hand rule, which states that if the thumb of your right hand points in the direction of the current, and the fingers point in the direction of the magnetic field, then the palm of your hand will point in the direction of the magnetic force.

## What factors affect the strength of magnetic force on a loop?

The strength of magnetic force on a loop depends on the strength of the magnetic field, the amount of current flowing through the loop, and the size and orientation of the loop.

## Can magnetic force on a loop be used for any practical applications?

Yes, magnetic force on a loop is used in various applications such as electric motors, generators, and particle accelerators. It is also used in magnetic levitation and magnetic resonance imaging (MRI) technology.

## How can the direction of magnetic force on a loop be changed?

The direction of magnetic force on a loop can be changed by either changing the direction of the current flowing through the loop or by changing the orientation of the loop with respect to the magnetic field.

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