# Force on a copper loop entering into a magnetic Field B with speed v

• spsch
In summary, the problem was that the current needed to be induced in order for the magnetic field to work, and the length of the wire that was exposed to the field was used to calculate the current. The wire resistance was calculated using the equation R = \dfrac{\rho L}{\pi r^2}.
spsch
Homework Statement
A rectangular copper loop is entering a magnetic field B with speed v. What is the Force against the loop's motion?
B = 0.03 T
diameter of the cooper string is 0.4 mm
and v = 5 m/s

Loops dimensions are length 10cm, width 5cm.
Relevant Equations
## V= (change in magnetic flux) / (change in time) ## (I'm not sure about the greek letter, is it phi?)
F = ILB
V = IR
Hi, second problem in one evening, I'm sorry!

But I'm also not quite sure if I did this one right.

I had thought I need lenz's law but there is no current before entering the field so I just use the induced Voltage?
My approach:
## V = \frac {B*A}{t} ##
## IR = \frac {B*A}{t} ## and ## A = v*t (1s) * width (0.05m) ##
so ## I = \frac{B*v*width}{R} ## and ## R = rho* \frac {2v+w}{pi*(0.0004)^2} ##
then ## I = \frac{B*v*width*(pi*(0.0002)^2)}{2v+w} ##
Because ## F = ILB ## I have after canceling some terms:
## F = \frac {B^2*pi*(\frac {d}{2})*width*v}{rho*(2*v+width)} ##

It seems overly complicated? Could someone maybe point to where I went wrong?

It looks good except for the wire resistance. The resistance of a wire is given by ##R=\dfrac{\rho L}{\pi r^2}##, where ##L## is the length of the wire and ##r## is its radius. What are these two quantities in this case? Specifically, why is the length ##2v+w##? Does the loop perimeter get to be longer when it moves faster? Also, in the last equation for the force you forgot to square ##(\frac{d}{2}).##

spsch, Michael Price and berkeman
Hi Kuruman! Thank you for helping me on this post as well.

Originally I only had w as L when I first worked on the problem. Because only this section of the wire experiences a net force.
But since the current is induced through all the wire I thought I should use the length that is exposed to the magnetic field.

Should I use the full length of the loop instead? (That kind of makes sense now that I think about it because the current should go through the whole loop, right?)

So then L would be ## 2*width + 2*length ## or 0.3 meters.
R is correct I believe, d/2. And yes, I missed to square it in my post here, thanks for pointing this out too. I wanted to correct but it doesn't let me anymore.

spsch said:
Should I use the full length of the loop instead? (That kind of makes sense now that I think about it because the current should go through the whole loop, right?)
Right. The length of wire has the resistance it has even when no current is running through it.

spsch
kuruman said:
Right. The length of wire has the resistance it has even when no current is running through it.
Thank you!

## What is the definition of force on a copper loop entering into a magnetic field?

The force on a copper loop entering into a magnetic field is the force exerted on the loop due to the interaction between the magnetic field and the current flowing through the loop.

## How is the force on a copper loop entering into a magnetic field calculated?

The force on a copper loop entering into a magnetic field is calculated using the formula F = BIL, where B is the strength of the magnetic field, I is the current flowing through the loop, and L is the length of the loop.

## What is the direction of the force on a copper loop entering into a magnetic field?

The direction of the force on a copper loop entering into a magnetic field is perpendicular to both the direction of the magnetic field and the direction of the current flowing through the loop. This is known as the right-hand rule.

## How does the speed of the copper loop entering into a magnetic field affect the force?

The speed of the copper loop entering into a magnetic field has a direct effect on the force. The faster the loop enters the field, the larger the force will be. This is because the rate of change of magnetic flux, which is directly related to the speed of the loop, affects the magnitude of the force.

## What are some real-life applications of the force on a copper loop entering into a magnetic field?

The force on a copper loop entering into a magnetic field has many practical applications, such as in electric motors and generators. It is also used in devices like speakers and headphones, which use a magnetic field to produce sound. Additionally, this force is utilized in medical imaging techniques like magnetic resonance imaging (MRI).

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