At what distance on the axis, from the centre of a circular current carrying coil of radius $r$, the magnetic field becomes $1 / 8$ th of the magnetic field at centre?
Medium
Download our app for free and get started
(c)
$\frac{1}{8} \frac{\mu_0 i}{2 r}=\frac{\mu_0 / r^2}{2\left(r^2+x^2\right)^{3 / 2}}$
$\Rightarrow\left(r^2+x^2\right)^{3 / 2}=8 r^3$
$\Rightarrow\left(r^2+x^2\right)=\left(8 r^3\right)^{2 / 3}$
$\Rightarrow r^2+x^2=4 r^2$
$\Rightarrow 3 r^2=x^2$
$\Rightarrow x=r \sqrt{3}$
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
- 1To Verify Ohm's law, a student is provided with a test resistor $\mathrm{R}_{\mathrm{T}}$, a high resistance $\mathrm{R}_1$, a small resistance $\mathrm{R}_2$, two identical galvanometers $\mathrm{G}_1$ and $\mathrm{G}_2$, and a variable voltage source $\mathrm{V}$. The correct circuit to carry out the experiment isView Solution
- 2View SolutionA proton is moves on circular path with its constant angular speed then correct relation between its magnetic moment and angular momentum
- 3One of the two small circular coils, (none of them having any self- inductance) is suspended with a $V-$ shaped copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both the coils are connected in series with a $dc$ supply. The coils are found to attract each other with a force. Which one of the following statements is incorrect ?View Solution
- 4There are $50$ $turns$ of a wire in every $cm$ length of a long solenoid. If $4\, ampere$ current is flowing in the solenoid, the approximate value of magnetic field along its axis at an internal point and at one end will be respectivelyView Solution
- 5A moving coil galvanometer has $50$ turns and each turn has an area $2 \times 10^{-4} m ^2$. The magnetic field produced by the magnet inside the galvanometer is $0.02 T$. The torsional constant of the suspension wire is $10^{-4} N m rad ^{-1}$. When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by $0.2$ rad. The resistance of the coil of the galvanometer is $50 \Omega$. This galvanometer is to be converted into an ammeter capable of measuring current in the range $0-1.0 A$. For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms, is. . . . . .View Solution
- 6At what distance for a long straight wire carrying a current of $12\, A$ will the magnetic field be equal to $3 \times 10^{-5} Wb / m ^{2}$ ?View Solution
- 7View SolutionA very high magnetic field is applied to a stationary charge. Then the charge experiences
- 8An electron is travelling along the $x$-direction. It encounters a magnetic field in the $y$-direction. Its subsequent motion will beView Solution
- 9Two particles $A$ and $B$ having equal charges $+6\,C$, after being accelerated through the same potential difference, enter in a region of uniform magnetic field and describe circular paths of radii $2\,cm$ and $3\,cm$ respectively. The ratio of mass of $A$ to that of $B$ isView Solution
- 10The magnetic field at the center of current carrying circular loop is $B _{1}$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_{2}$. The value of $B_{1} / B_{2}$ will be.View Solution