A thin rod is bent in the shape of a small circle of radius 'r'. If the charge per unit length of the rod is

Q: A thin rod is bent in the shape of a small circle of radius $'r'$. If the charge per unit length of the rod is $'\sigma ',$ and if the circle is rotated about its axis at the rate of $'n'$ rotation per second, the magnetic induction at a point on the axis at a large distance $'y'$ from the centre is

a ${{\text{B}}_y} = \frac{{{\mu _0}{\text{I}}{{\text{R}}^2}}}{{2{{\left( {{{\text{y}}^2} + {{\text{R}}^2}} \right)}^{3/2}}}} = \frac{{{\mu _0}{\text{I}}{{\text{R}}^2}}}{{2{{\text{y}}^3}}}({\text{forY}} > > > {\text{R}})$ $\left[\because I=\frac{q}{t}=\frac{\sigma(2 \pi R)}{t}=\sigma(2 \pi R) n\right]$ $\mathrm{B}_{\mathrm{y}}=\frac{\mu_{0} \sigma(2 \pi \mathrm{R}) \mathrm{nR}^{2}}{2 \mathrm{y}^{3}}=\frac{\mu_{0} \sigma \pi \mathrm{R}^{3} \mathrm{n}}{\mathrm{y}^{3}}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A thin rod is bent in the shape of a small circle of radius $'r'$. If the charge per unit length of the rod is $'\sigma ',$ and if the circle is rotated about its axis at the rate of $'n'$ rotation per second, the magnetic induction at a point on the axis at a large distance $'y'$ from the centre is

A$\frac{{{\mu _0}\pi {r^3}n\sigma }}{{{y^3}}}$
B$\frac{{2{\mu _0}\pi {r^3}n\sigma }}{{{y^3}}}$
C$\frac{{\left( {\frac{{{\mu _0}}}{{4\pi }}} \right){r^3}n\sigma }}{{{y^3}}}$
D$\frac{{\left( {\frac{{{\mu _0}}}{{2\pi }}} \right){r^3}n\sigma }}{{{y^3}}}$

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
Consider a galvanometer shunted with $5\, \Omega$ resistance and $2\, \%$ of current passes through it.

What is the resistance of the given galvanometer? (In $\Omega$)
View Solution
2
A straight section $PQ$ of a circuit lies along the $X$-axis from $x = - \frac{a}{2}$ to $x = \frac{a}{2}$ and carries a steady current $i$. The magnetic field due to the section $PQ$ at a point $X = + a$ will be
View Solution
3
A loop in form of four connected semi-circular wires carrying current $I$ lies in the $x-y$ plane as shown in the figure. The unit vector $\hat k$ is coming out of the plane of the paper. The magnetic moment of the current loop is
View Solution
4
$PQRS$ is a square loop made of uniform conducting wire the current enters the loop at $P$ and leaves at $S$. Then the magnetic field will be
View Solution
5
Mark the correct statement
View Solution
6
A long thin walled pipe of radius $R$ carries a current $I$ along its length. The current density is uniform over the circumference of the pipe. The magnetic field at the center of the pipe due to quarter portion of the pipe shown, is
View Solution
7
A galvanometer of resistance $100 \Omega$ when connected in series with $400 \Omega$ measures a voltage of upto $10 \mathrm{~V}$. The value of resistance required to convert the galvanometer into ammeter to read upto $10 \mathrm{~A}$ is $\mathrm{x} \times 10^{-2} \Omega$. The value of $\mathrm{x}$ is :
View Solution
8
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
9
The magnetic field at the centre of a circular coil of radius $I$, due to current I flowing through it, is $B$. The magnetic field at a point along the axis at a distance $\frac{r}{2}$ from the centre is
View Solution
10
A negative charge is coming towards the observer. The direction of the magnetic field produced by it will be (as seen by observer)
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free