Electromagnetic repulsion force

In summary, a small conducting loop with negligible self inductance and a radius of a is placed in the y-z plane with its centre at x = 0 and its axis on the x axis. An infinitesimally small bar magnet with a dipole moment of ##\vec{M}## and moving at a speed v in the x direction causes a magnetic field of ##B = \dfrac{μ_0M}{2πx^3}## at the centre of the ring. The induced current in the loop is ##i = \dfrac{3μ_0Ma^2v}{2x^4R}## and the resulting force on the loop is ##\vec{
  • #1
erisedk
374
7

Homework Statement


An infinitesimally small bar magnet of dipole moment ##\vec{M}## is pointing and moving with the speed v in the x direction. A small closed circular conducting loop of radius a and negligible self inductance lies in the y-z plane with its centre at x = 0, and its axis coinciding with the x axis. Find the force opposing the motion of the magnet, if the resistance of the loop is R. Assume that the distance x of the magnet from the centre of the loop is much greater than a.

Homework Equations

The Attempt at a Solution


Magnetic field due to the magnet of dipole moment ##\vec{M}## on its axis at a distance x (i.e. at the centre of the ring) = ##B = \dfrac{2μ_0M}{4πx^3} = \dfrac{μ_0M}{2πx^3}##

##φ_{ring} = B.A = \dfrac{μ_0M}{2πx^3}.πa^2 = \dfrac{μ_0Ma^2}{2x^3}##

##|ε| = \dfrac{dφ}{dt} = \dfrac{3μ_0Ma^2v}{2x^4}##

##i## (flowing in ring) = ## \dfrac{3μ_0Ma^2v}{2x^4R}##

After this, I'm confused.
My attempt:
## F = ilB = \dfrac{3μ_0Ma^2v}{2x^4R}.2a.\dfrac{μ_0M}{2πx^3}##

## F = \dfrac{3μ_0M^2a^3v}{2x^7Rπ}##

This answer is wrong. It is surely due to me having taken l = 2a. Usually, when we consider arbitrarily shaped conductors in a uniform magnetic field (it is uniform on the ring as x>>a), the force, i.e.
##\vec{F} = \int I \vec{dL} × \vec{B} = I \vec{L} × \vec{B}## where ##\vec{L}## is the length vector joining initial and final points of the conductor. Now, in case of a circular loop, this should've been zero. But that is clearly wrong as there is some force due to lenz's law. I believe it is wrong because the lorentz force equation can't be applied to currents induced due to the magnetic field. It can only be used when we have a current carrying conductor placed in an external magnetic field (I think). In any case, I'm not sure what to do. Please help.
 
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  • #2
I think your expression for the current looks good. If you approximate the magnetic field as purely in the x direction at the loop, would there be any net magnetic force on the loop? Consider the direction of the magnetic force on a small element of length of the loop if the B field has only an x component.
 
  • #3
TSny said:
If you approximate the magnetic field as purely in the x direction at the loop, would there be any net magnetic force on the loop?

Zero, because magnetic force on a coil of wire is always zero in a uniform magnetic field?
 
  • #4
Yes. For the force calculation, you'll need to take into account that B is not actually uniform.
 
  • #5
How do I start?
 
  • #6

What is electromagnetic repulsion force?

Electromagnetic repulsion force is a fundamental force in nature that describes the interaction between two objects with electric charge. It is a repulsive force that occurs when two objects with the same type of charge (either positive or negative) are brought close together.

How does electromagnetic repulsion force work?

Electromagnetic repulsion force works through the exchange of virtual photons between two charged particles. These virtual photons act as carriers of the force, pushing the particles apart when they have the same charge.

What are some examples of electromagnetic repulsion force in everyday life?

Some examples of electromagnetic repulsion force in everyday life include the repulsion between two magnets with the same pole facing each other, the repulsion between two balloons with the same charge, and the repulsion between two negatively charged particles in an atom.

How does the strength of electromagnetic repulsion force depend on distance?

The strength of electromagnetic repulsion force is inversely proportional to the square of the distance between two charged particles. This means that as the distance between the particles increases, the force between them decreases.

How does electromagnetic repulsion force differ from gravitational force?

Electromagnetic repulsion force is a force between two charged particles, while gravitational force is a force between two objects with mass. Additionally, gravitational force is always attractive, while electromagnetic repulsion force can be either attractive or repulsive depending on the charges of the particles involved.

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