0.12 Magnetic force on a conductor  (Page 4/5)

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For such situation involving nonlinear wire, we prefer to have an expression for a infinitesimally small length of wire. This consideration of very small length of wire guarantees that the wire element is straight. Following the similar argument as for a straight wire, the magnetic force on an infinitesimally small length of wire is :

$\mathbf{F}=Iđ\mathbf{L}X\mathbf{B}$

We can, then, use this expression and integrate along non-linear wire. Of course, such calculation will depend on the possibility to divide the given wire into segments for which integration of this expression is possible.

Current element and moving charge

We have pointed out the equivalent role of current element and moving charge in the context of production or setting up of magnetic field. An inspection of the expression of magnetic force on a charge and a current element indicate that the equivalence is true also in the case of experiencing magnetic force. In the case of moving charge, the magnetic force is given by :

$F=q\left(\mathbf{v}X\mathbf{B}\right)$

On the other hand, the magnetic force on a small current carrying wire element is :

$\mathbf{F}=Iđ\mathbf{L}X\mathbf{B}$

Clearly, the term “q v ” and “Id L ” play the equivalent role in two cases.

Problem : An irregular shaped flexible wire loop of length “L” is placed in a perpendicular and uniform magnetic field “B” as shown in the figure below (The magnetic force represented by filled circle is perpendicular and out of the plane of drawing). Determine the tension in the loop if a current “I” is passed through it in anticlockwise direction.

Solution : The wire loop is flexible. There would be tension, provided the loop elements experience magnetic force in outward direction at all points on it. Applying Right hand thumb rule for any small segment of the loop, we find that the wire is indeed subjected to outward magnetic force. Clearly, the loop expands to become a circular loop. The radius of the circle is given by :

$2\pi r=L$ $⇒r=\frac{L}{2\pi }$

In order to determine tension in the wire, we consider a very small element of the circular loop. Let the loop element subtends an angle dθ at the center. Let “T” be the tension in the wire. It is clear that components of tension in the downward direction should be equal to magnetic force on the small wire element.

$2T\mathrm{sin}\frac{đ\theta }{2}={F}_{M}$

Since loop element is very small, we approximate as :

$\mathrm{sin}\frac{đ\theta }{2}\approx \frac{đ\theta }{2}$

Further, we can consider the small loop element to be a straight wire for the calculation of magnetic force. Now, the magnetic force on the loop element is :

${F}_{M}=IBđL=IBrđ\theta$

Substituting in the equilibrium equation,

$⇒2T\frac{đ\theta }{2}=IBrd\theta$ $⇒T=IBr$

Again substituting for the radius of circle, we have :

$⇒T=\frac{ILB}{2\pi }$

Magnetic force between parallel wires carrying current

The situation here is just an extension of the study of the magnetic force on a current carrying wire. The basic consideration here is that a wire carrying current can function in either of following two roles : (i) it produces magnetic field and (ii) it experiences magnetic force.

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
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kkk nice
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yes
Asali
I'm not good at math so would you help me
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what is the problem that i will help you to self with?
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China
Cied
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many many of nanotubes
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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anybody can imagine what will be happen after 100 years from now in nano tech world
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after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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silver nanoparticles could handle the job?
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not now but maybe in future only AgNP maybe any other nanomaterials
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can nanotechnology change the direction of the face of the world
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