# 0.4 Magnetic field due to current in a circular wire  (Page 3/5)

 Page 3 / 5

Problem : Calculate magnetic field at the center O for the current flowing through wire segment as shown in the figure. Here, current through wire is 10 A and radius of the circular part is 0.1 m.

Solution : Magnetic field at O is contributed by long straight wire and circular wire. The direction of magnetic field at O due to straight part of the wire is into the plane of drawing as obtained by applying Right hand thumb rule for straight wire. The direction of current in the circular part is anticlockwise and hence magnetic field due to this part is out of the plane of drawing as obtained by applying Right hand thumb rule for circular wire.

The magnitude of magnetic field due to circular wire is :

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

The magnitude of magnetic field due to straight wire is :

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

Hence, magnitude of magnetic field at O is algebraic sum of two magnetic fields (we consider outward direction as positive) :

$B={B}_{C}-{B}_{S}=\frac{{\mu }_{0}I}{2R}-\frac{{\mu }_{0}I}{2\pi R}$

Putting values :

$⇒B=\frac{4\pi {10}^{-7}X10}{2X0.1}-\frac{4\pi {10}^{-7}X10}{2\pi X0.1}$ $⇒B=62.9X{10}^{-6}-20X{10}^{-6}=42.9\phantom{\rule{1em}{0ex}}\mu T$

The net magnetic field is acting out of the plane of paper.

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

The magnitude of magnetic field due to current in arc shaped wire can be obtained by integrating Biot-Savart expression in an appropriate range. Now, the integral set up for current in circular wire is :

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

Circular arc is generally referred in terms of the angle θ, it subtends at the center of the circle. From geometry, we know that :

$đl=Rđ\theta$ Substituting in the integral and taking the constant R out of the integral, we have :

$B=\frac{{\mu }_{0}I}{4\pi R}\int đ\theta$ $⇒B=\frac{{\mu }_{0}I\theta }{4\pi R}$

This is the expression for the magnitude of magnetic field due to current in an arc which subtends an angle θ at the center. Note that the expression is true for the circle for which θ = 2π and magnetic field is :

$⇒B=\frac{{\mu }_{0}IX2\pi }{4\pi R}=\frac{{\mu }_{0}I}{2R}$

Problem : Find the magnetic field at the corner O due to current in the wire as shown in the figure. Here, radius of curvature is 0.1 m for the quarter circle arc and current is 10 A.

Solution :

Here the straight line wire segment AB and CD when extended meet at O. As such, there is no magnetic field due to current in these segments. The magnetic field at O is, therefore, solely due to magnetic field due to quarter arc AC. The arc subtends an angle π/2 at its center i.e O. Now,

$B=\frac{{\mu }_{0}I\theta }{4\pi R}$

Putting values, we have :

$⇒B=\frac{{10}^{-7}X10X\pi }{0.1X2}=0.157X{10}^{-6}=0.157\phantom{\rule{1em}{0ex}}\mu T$

Since current in the arc is anticlockwise, magnetic field is perpendicular and out of the plane of drawing.

## Current in straight wire .vs. current in circular wire

A length of wire, say L, is given and it is asked to maximize magnetic field in a region due to a current I in the wire. Which configuration would we consider – a straight wire or a circular wire? Let us examine the magnetic fields produced by these two configurations.

If we bend the wire in the circle, then the radius of the circle is :

who was the first nanotechnologist
k
Veysel
technologist's thinker father is Richard Feynman but the literature first user scientist Nario Tagunichi.
Veysel
Norio Taniguchi
puvananathan
Interesting
Andr
I need help
Richard
anyone have book of Abdel Salam Hamdy Makhlouf book in pdf Fundamentals of Nanoparticles: Classifications, Synthesis
what happen with The nano material on The deep space.?
It could change the whole space science.
puvananathan
the characteristics of nano materials can be studied by solving which equation?
sibaram
synthesis of nano materials by chemical reaction taking place in aqueous solvents under high temperature and pressure is call?
sibaram
hydrothermal synthesis
ISHFAQ
how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
STM - Scanning Tunneling Microscope.
puvananathan
Got questions? Join the online conversation and get instant answers!

#### Get Jobilize Job Search Mobile App in your pocket Now! By Tony Pizur By JavaChamp Team By John Gabrieli By OpenStax By Brooke Delaney By Qqq Qqq By OpenStax By OpenStax By Janet Forrester By OpenStax