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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 :

F = I đ L X 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 v X B

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

F = I đ L X 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.

An irregular shaped flexible wire loop in magnetic field

An irregular shaped flexible wire loop in magnetic field

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 :

An irregular shaped flexible wire loop in magnetic field

An irregular shaped flexible wire loop straightens up to acquire a circular shape due to magnetic force.

2 π r = L r = L 2 π

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.

The tension in the circular loop carrying current

The tension in the circular loop carrying current

2 T sin đ θ 2 = F M

Since loop element is very small, we approximate as :

sin đ θ 2 đ θ 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 = I B đ L = I B r đ θ

Substituting in the equilibrium equation,

2 T đ θ 2 = I B r d θ T = I B r

Again substituting for the radius of circle, we have :

T = I L B 2 π

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.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
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
I'm not sure why it wrote it the other way
I got X =-6
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
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
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Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Electricity and magnetism. OpenStax CNX. Oct 20, 2009 Download for free at http://cnx.org/content/col10909/1.13
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