Two circular coils X and Y, having equal number of turns, carry equal currents in the same sense and subtend same solid angle at point

Q: Two circular coils $X$ and $Y$, having equal number of turns, carry equal currents in the same sense and subtend same solid angle at point $O$. If the smaller coil, $X$ is midway between $O$ and $Y$, then if we represent the magnetic induction due to bigger coil $Y$ at $O$ as $BY$ and that due to smaller coil $X$ at $O$ as $BX$ , then

c (c) Magnetic field at $O$ due to bigger coil $Y$, is ${B_Y} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi i{{(2r)}^2}}}{{{{\{ {d^2} + {{(2r)}^2}\} }^{3/2}}}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{8\pi i{r^2}}}{{{{({d^2} + 4{r^2})}^{3/2}}}}$ Magnetic field at $O$ due to smaller coil $X$ is ${B_X} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi i{r^2}}}{{{{\left\{ {{{\left( {\frac{d}{2}} \right)}^2} + {r^2}} \right\}}^{3/2}}}} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{16\pi i{r^2}}}{{{{({d^2} + 4{r^2})}^{3/2}}}}$ $==>$ $\;\frac{{{B_Y}}}{{{B_X}}} = \frac{1}{2}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

Two circular coils $X$ and $Y$, having equal number of turns, carry equal currents in the same sense and subtend same solid angle at point $O$. If the smaller coil, $X$ is midway between $O$ and $Y$, then if we represent the magnetic induction due to bigger coil $Y$ at $O$ as $BY$ and that due to smaller coil $X$ at $O$ as $BX$ , then

A$\frac{{{B_Y}}}{{{B_X}}} = 1$
B$\frac{{{B_Y}}}{{{B_X}}} = 2$
C$\frac{{{B_Y}}}{{{B_X}}} = \frac{1}{2}$
D$\frac{{{B_Y}}}{{{B_X}}} = \frac{1}{4}$

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
The magnetic field existing in a region is given by $\vec{B}=B_0\left(1+\frac{x}{l}\right) \hat{k}$. A square loop of edge I and carrying a current $i$, is placed with its edge parallel to the $x-y$ axes. Find the magnitude of the net magnetic force experienced by the loop
View Solution
2
A non-planar loop of conducting wire carrying a current $I$ is placed as shown in the figure. Each of the straight sections of the loop is of length $2a$. The magnetic field due to this loop at the point $P$ $(a,0,a)$ points in the direction
View Solution
3
Two parallel, long wires are kept $0.20\,m$ apart in vacuum, each carrying current of $x$ in the same direction. If the force of attraction per meter of each wire is $2 \times 10^{-6}\,N$, then the value of $x$ is approximately
View Solution
4
An electron is moving along positive $x$-axis.Auniform electric field exists towards negative $y$-axis. What should be the direction of magnetic field of suitable magnitude so that net force of electron is zero
View Solution
5
A circular coil of $30$ turns and radius $8.0\, cm$ carrying a current of $6.0\, A$ is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0\, T$. The field lines make an angle of $60^o$ with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.....$Nm$
View Solution
6
A thin hollow copper pipe carries direct current than which is incorrect
View Solution
7
A teacher in his physics laboratory allotted an experiment to determine the resistance $(G)$ of a galvanometer. Students took the observations for $\frac{1}{3}$ deflection in the galvanometer. Which of the below is true for measuring value of $G$ $?$
View Solution
8
$A$ galvanometer may be converted into ammeter or voltmeter. In which of the following cases the resistance of the device will be the largest ? (Asssume maximum range of galvanometer $= 1\, mA$)
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
The dimension of the magnetic field intensity $B$ is
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free