# 0.4 Magnetic field due to current in a circular wire  (Page 2/5)

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## Current in circular wire and magnet

The directional attributes of the magnetic field due to current in circular wire have an important deduction. If the current in a circular loop is anticlockwise when we look from one end (face), then the same current is clockwise when we look from opposite end (face). What it means that if direction of magnetic field is towards you from one face, then the direction of magnetic field is away from you from the other end and vice versa.

The magnetic lines of force enters from the face in which current is clockwise and exits from the face in which current is anticlockwise. This is exactly the configuration with real magnet. The anticlockwise face of the circular wire is equivalent to north pole and clockwise face is equivalent to south pole of the physical magnet. For this reason, a current in a circular wire is approximately equivalent to a tiny bar magnet.

## Magnitude of magnetic field due to current in circular wire

Evaluation of Biot-Savart expression at the center of circle for current in circular wire is greatly simplified. There are threefold reasons :

1: The directions of magnetic fields due to all current elements at the center are same just as in the case of straight wire.

2: The linear distance (r) between current length element (d l ) and the point of observation (center of circular wire) is same for all current elements.

3: The angle between current length element vector (d l ) and displacement vector ( R ) is right angle for all current elements. Recall that angle between tangent and radius of a circle is right angle at all positions on the perimeter of a circle.

The magnitude of magnetic field due to a current element according to Biot-Savart law is given by :

$\mathrm{đB}=\frac{{\mu }_{0}}{4\pi }\frac{Iđl\mathrm{sin}\theta }{{r}^{2}}$

But, θ=90° and sin90°=1. Also, r = R = Radius of circular wire.

$⇒\mathrm{đB}=\frac{{\mu }_{0}}{4\pi }\frac{Iđl}{{R}^{2}}$

All parameters except "đl" in the right hand expression of the equation are constants and as such they can be taken out of the integral.

$B=\int \mathrm{đB}=\frac{{\mu }_{0}I}{4\pi {R}^{2}}\int đl$

The integration of dl over the complete circle is equal to its perimeter i.e. 2πR.

$⇒B=\frac{{\mu }_{0}I}{4\pi {R}^{2}}X2\pi R=\frac{{\mu }_{0}I}{2R}$

If the wire is a coil having N circular turns, then magnetic filed at the center of coil is reinforced N times :

$B=\frac{{\mu }_{0}NI}{2R}$

Problem : A thin ring of radius “R” has uniform distribution of charge, q, on it. The ring is made to rotate at an angular velocity “ω” about an axis passing through its center and perpendicular to its plane. Determine the magnitude of magnetic field at the center.

Solution : A charged ring rotating at constant angular velocity is equivalent to a steady current in circular wire. We need to determine this current in order to calculate magnetic field. For this, let us concentrate at any cross section of the ring. All the charge passes through this cross section in one time period of revolution. Thus, equivalent current is :

$I=\frac{q}{T}=\frac{q\omega }{2\pi }$

Now, magnetic field due to steady current in circular wire is :

$B=\frac{{\mu }_{0}I}{2R}$

Substituting for current, we have :

$⇒B=\frac{{\mu }_{0}q\omega }{4\pi R}$

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
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Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
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I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
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what is the stm
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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LITNING
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
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if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
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analytical skills graphene is prepared to kill any type viruses .
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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write examples of Nano molecule?
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The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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what school?
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biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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