Two 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 $\qquad$
JEE MAIN 2024, Diffcult
Download our app for free and get started
$\mathrm{B}_{\mathrm{A}}=\frac{\mu_0 \mathrm{i}}{2 \pi \mathrm{r}}+\frac{\mu_0(2 \mathrm{i})}{2 \pi(3 \mathrm{r})}=\frac{5 \mu_0 \mathrm{i}}{6 \pi \mathrm{r}}$
$\mathrm{B}_C=\frac{\mu_0(2 \mathrm{i})}{2 \pi \mathrm{r}}+\frac{\mu_0 \mathrm{i}}{2 \pi(3 \mathrm{r})}=\frac{7 \mu_0 \mathrm{i}}{6 \pi \mathrm{r}}$
$\therefore \frac{\mathrm{B}_A}{\mathrm{~B}_C}=\frac{5}{7}$
$\therefore \mathrm{x}=5$
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
- 1A helium nucleus makes a full rotation in a circle of radius $0.8$ metre in two seconds. The value of the magnetic field $B$ at the centre of the circle will beView Solution
- 2A $50\,\Omega $ resistance is connected to a battery of $5\,V$. A galvanometer of resistance $100\, \Omega $ is to be used as an ammeter to measure current through the resistance, for this a resistance $r_s$ is connected to the galvanometer. Which of the following connections should be employed if the measured current is within $1\% $ of the current without the ammeter in the circuit ?View Solution
- 3A voltmeter of resistance $20000\,\Omega$ reads $5$ volt. To make it read $20$ volt, the extra resistance required isView Solution
- 4An arrangement with a pair of quarter circular coils of radii $r$ and $R$ with a common centre $C$ and carrying a current $I$ is shown in the figure. The permeability of free space is $\mu_0$. The magnetic field at $C$ isView Solution
- 5View SolutionIdentical currents flow in two perpendicular wires, as shown in the figure. The wires are very close but do not touch. The magnetic field can be zero:
- 6A car of mass $1000\,kg$ negotiates a banked curve of radius $90\,m$ on a fictionless road. If the banking angle is $45^o$, the speed of the car is ......... $ms^{-1}$View Solution
- 7A proton and an $\alpha$ -particle, having kinetic energies $K _{ p }$ and $K _{\alpha},$ respectively, enter into $a$ magnetic field at right angles.View Solution
The ratio of the radii of trajectory of proton to that of $\alpha$ -particle is $2: 1 .$ The ratio of $K _{ p }: K _{\alpha}$ is :
- 8An infinitely long wire carrying current $I$ is along $Y$ axis such that its one end is at point $A(0, b)$ while the wire extends upto $+ \infty .$ The magnitude of magnetic field strength at point $(a, 0)$View Solution
- 9The current in the windings on a toroid is $2.0\,A$. There are $400$ $turns$ and the mean circumferential length is $40\,cm$. If the inside magnetic field is $1.0\,T$, the relative permeability is near toView Solution
- 10The magnetic induction at the centre of a current carrying circular coil of radius $10\, cm$ is $5\sqrt 5 \,times$ the magnetic induction at a point on its axis. The distance of the point from the centre of the coil (in $cm$) isView Solution