Magnetic fields at two points on the axis of a circular coil at a distance of $0.05\, m$ and $0.2\, m$ from the centre are in the ratio $8: 1.$ The radius of coil is .......... $m$
JEE MAIN 2021, Diffcult
Download our app for free and get started
We know, the magnetic field on the axis of a current carrying circular ring is given by
$B =\frac{\mu_{0}}{4 \pi} \frac{2 NIA }{\left( R ^{2}+ x ^{2}\right)^{3 / 2}}$
$\therefore \frac{ B _{1}}{ B _{2}}=\frac{8}{1}=\left[\frac{ R ^{2}+(0.2)^{2}}{ R ^{2}+(0.05)^{2}}\right]^{3 / 2}$
$4\left[ R ^{2}+(0.05)^{2}\right]=\left[ R ^{2}+(0.2)^{2}\right]$
$4 R ^{2}- R ^{2}=(0.2)^{2}-4 \times(0.05)^{2}$
$4 R ^{2}- R ^{2}=(0.2)^{2}-(0.1)^{2}$
$3 R ^{2}=0.3 \times 0.1$
$R ^{2}=(0.1)^{2} \Rightarrow R =0.1$
Download our appand 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.*
Similar Questions
- 1The magnetic induction due to an infinitely long straight wire carrying a current $i$ at a distance $r$ from wire is given byView Solution
- 2A particle of mass $m = 1.67 \times 10^{-27}\, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $1$ $tesla$ along the direction shown in the figure. If the direction of the magnetic field is along the outward normal to the plane of the paper, then the time spent by the particle in the region of the magnetic field after entering it at $C$ is nearly :-......$ns$View Solution
- 3The magnetic field at a distance $r$ from a long wire carrying current $i$ is $0.4\, Tesla$. The magnetic field at a distance $2r$ is......$Tesla$View Solution
- 4The current of $5 \mathrm{~A}$ flows in a square loop of sides $1$ $\mathrm{m}$ is placed in air. The magnetic field at the centre of the loop is $\mathrm{X} \sqrt{2} \times 10^{-7} \mathrm{~T}$. The value of $\mathrm{X}$ is____.View Solution
- 5Two resistances $R_1=X \Omega$ and $R_2=1 \Omega$ are connected to a wire $A B$ of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 mm$ at $A$ to $1 mm$ at $B$. A galvanometer ($G$) connected to the center of the wire, $50 cm$ from each end along its axis, shows zero deflection when $A$ and $B$ are connected to a battery. The value of $X$ is. . . . .View Solution
- 6The correct curve between the magnetic induction $(B)$ along the axis of a long solenoid due to current flow $i$ in it and distance $x$ from one end is :View Solution
- 7Two parallel long current carrying wire separated by a distance $2 \mathrm{r}$ are shown in the figure. The ratio of magnetic field at $\mathrm{A}$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is $\qquad$View Solution
- 8View SolutionA galvanometer can be used as a voltmeter by connecting a
- 9View SolutionOne Tesla is equal to
- 10An ammeter of $5\, ohm$ resistance can read $5 \,mA$. If it is to be used to read $100\, volts$, how much resistance is to be connected in series ............... $\Omega $View Solution