A wire in the form of a square of side ‘a’ carries a current i. Then the magnetic induction at the centre of the square

Q: A wire in the form of a square of side ‘$a$’ carries a current $i$. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space =${\mu _o}$)

c (c) ${B_0} = 4 \times \frac{{{\mu _0}}}{{4\pi }} \times \frac{i}{{\left( {a/2} \right)}}(\sin 45^\circ + \sin 45^\circ )$ $ = 4 \times \frac{{{\mu _0}}}{{4\pi }} \times \frac{{2i}}{a} \times \frac{2}{{\sqrt 2 }}$ $ = \frac{{{\mu _0}i2\sqrt 2 }}{{\pi a}}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A wire in the form of a square of side ‘$a$’ carries a current $i$. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space =${\mu _o}$)

A$\frac{{{\mu _0}i}}{{2\pi a}}$
B$\frac{{{\mu _0}i\sqrt 2 }}{{\pi a}}$
C$\frac{{2\sqrt 2 {\mu _o}i}}{{\pi a}}$
D$\frac{{{\mu _0}i}}{{\sqrt 2 \pi \,a}}$

Diffcult

STD 11 Science
NEET
STD 12 - 4. Moving charges and magnetism
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
An $\alpha - $ particle travels in a circular path of radius $0.45\, m$ in a magnetic field $B = 1.2\,Wb/{m^2}$ with a speed of $2.6 \times {10^7}\,m/\sec $. The period of revolution of the $\alpha - $ particle is
View Solution
2
A wire $X$ of length $50\; cm$ carrying a current of $2\,A$ is placed parallel to a long wire $Y$ of length $5\,m$. The wire $Y$ carries a current of $3\,A$. The distance between two wires is $5\,cm$ and currents flow in the same direction. The force acting on the wire $Y$ is.
View Solution
3
When a $12\,\Omega $ resistor is connected with a moving coil galvanometer then its deflection reduces from $50$ divisions to $10$ divisions. The resistance of the galvanometer is ............. $\Omega $
View Solution
4
In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a
View Solution
5
A square coil of side $10\; cm$ consists of $20$ turns and carries a current of $12\; A$. The coil is suspended vertically and the normal to the plane of the coil makes an angle of $30^o$ with the direction of a uniform horizontal magnetic field of magnitude $0.80 \;T$. What is the magnitude of torque (in $N\;m$) experienced by the coil?
View Solution
6
Due to the flow of current in a circular loop of radius $R$, the magnetic induction produced at the centre of the loop is $B$. The magnetic moment of the loop is $({\mu _0} = {\rm{permeability}}\,{\rm{constant)}}$
View Solution
7
A current $I$ flows in an infinitely long wire with cross-section in the form of a semicircular ring of radius $R$. The magnitude of the magnetic induction along its axis is
View Solution
8
Two protons $A$ and $B$ move parallel to the $x$-axis in opposite directions with equal speeds $v$. At the instant shown, the ratio of magnetic force and electric force acting on the proton $A$ is ( $c=$ speed of light in vacuum)
View Solution
9
The earth’s magnetic field at a given point is $0.5 \times {10^{ - 5}}\,Wb{\rm{ - }}{m^{ - 2}}$. This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius $5.0\,cm$. The current required to be flown in the loop is nearly......$A$
View Solution
10
A disc of radius $r$ and carrying positive charge $q$ is rotating with an angular speed $l$ in a uniform magnetic field $B$ about a fixed axis as shown in figure, such that angle made by axis of disc with magnetic field is $\theta $. Torque applied by axis on the disc is
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free