Question:
A circular current carrying coil has a radius $R$. The distance from the centre of the coil on the axis, where the magnetic induction will be $\frac{1}{8}$th to its value at the centre of the coil is
A circular current carrying coil has a radius $R$. The distance from the centre of the coil on the axis, where the magnetic induction will be $\frac{1}{8}$th to its value at the centre of the coil is
Updated On: Apr 26, 2024
- $\frac{R}{\sqrt{3}}$
- $R \sqrt{3}$
- $2 \sqrt{3} R $
- $\frac{2}{\sqrt{3}} R $
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
$\frac{B_{\text {centre }}}{B_{\text {axis }}}=\left(1+\frac{x^{2}}{R^{2}}\right)^{3 / 2}$
Also,
$B_{\text {axis }} =\frac{1}{8} B_{\text {centre }}$
$\frac{8}{1} =\left(1+\frac{x^{2}}{R^{2}}\right)^{3 / 2}$
$4 =1+\frac{x^{2}}{R^{2}}$
$3=\frac{x^{2}}{R^{2}}$
$x^{2} =3 R^{2}$
$x =\sqrt{3} R$
Also,
$B_{\text {axis }} =\frac{1}{8} B_{\text {centre }}$
$\frac{8}{1} =\left(1+\frac{x^{2}}{R^{2}}\right)^{3 / 2}$
$4 =1+\frac{x^{2}}{R^{2}}$
$3=\frac{x^{2}}{R^{2}}$
$x^{2} =3 R^{2}$
$x =\sqrt{3} R$
Was this answer helpful?
0
0
Top Questions on Moving charges and magnetism
- The magnetic field existing in a region is given by \[\vec{B} = 0.2(1 + 2x)\hat{k} \, \text{T}.\]A square loop of edge \( 50 \, \text{cm} \) carrying \( 0.5 \, \text{A} \) current is placed in the \( x \)-\( y \) plane with its edges parallel to the \( x \)- and \( y \)-axes, as shown in the figure. The magnitude of the net magnetic force experienced by the loop is ______ \( \text{mN} \).
- JEE Main - 2024
- Physics
- Moving charges and magnetism
- Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [ \(\epsilon_0 \)is the permittivity of free space.]
- JEE Advanced - 2024
- Physics
- Moving charges and magnetism
- A freely suspended needle of a magnetic compass comes to rest along the geographic
- AP POLYCET - 2024
- Physics
- Moving charges and magnetism
- As shown in the figure, a very long conducting wire is bent in a semi-circular shape from A to B. The magnetic field at point P for steady current configuration is given by:
- NEET (UG) - 2023
- Physics
- Moving charges and magnetism
- A wire carrying a current I along the positive x-axis has length L. It is kept in a magnetic field \(\vec{B}=(2\vec{i}+3\vec j-4\vec k)T\). The magnitude of the magnetic force acting on the wire is:
- NEET (UG) - 2023
- Physics
- Moving charges and magnetism
View More Questions
Questions Asked in VITEEE exam
- Two identical blocks A and B, each of mass 'm' resting on a smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is
- VITEEE - 2023
- work, energy and power
- Assertion :
The binding energy of the nucleus increases with the increase in atomic number.
Reason :
Heavier elements have a greater number of non-radioactive isotopes than radioactive isotopes. - The half-life of radioactive radon is 3.8 days. The time at the end of which \(\frac{1}{20}th\) of the Radon sample will remain undecayed is (given log10e=0.4343)
- Which element has more electron gain enthalpy among chalcogen group?
- VITEEE - 2022
- sulphur
- Coin is tossed till heads is obtained what is expectation of no. of coin tosses
- VITEEE - 2022
- Random Variables
View More Questions
Concepts Used:
Moving Charges and Magnetism
Moving charges generate an electric field and the rate of flow of charge is known as current. This is the basic concept in Electrostatics. Another important concept related to moving electric charges is the magnetic effect of current. Magnetism is caused by the current.
Magnetism:
- The relationship between a Moving Charge and Magnetism is that Magnetism is produced by the movement of charges.
- And Magnetism is a property that is displayed by Magnets and produced by moving charges, which results in objects being attracted or pushed away.
Magnetic Field:
Region in space around a magnet where the Magnet has its Magnetic effect is called the Magnetic field of the Magnet. Let us suppose that there is a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them can be written as,
F = q [ E (r) + v × B (r)] ≡ EElectric +Fmagnetic
This force was based on the extensive experiments of Ampere and others. It is called the Lorentz force.