Moving Charges and Magnetism

A \(2\) amp current is flowing through two small circular copper coils having radii ratio \(1:2\). The ratio of their respective magnetic moments will be

An electron (mass \(9\times {10}^{-31}\mathrm{kg}\) and charge \(1.6\times {10}^{-19}\mathrm{C}\) ) moving with speed \(c/100\) (c = speed of light) is injected into a magnetic field B of magnitude \(9\times {10}^{-4}\mathrm{T}\) perpendicular to its direction of motion. We wish to apply an uniform electric field \(\vec{E}\) together with the magnetic field so that the electron does not deflect from its path. Then (speed of light \(\mathrm{c}=3\times {10}^{8}{\mathrm{ms}}^{-1}\) )

[NEET 2025]

A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to :

A. hold the sheet there if it is magnetic.

B. hold the sheet there if it is non-magnetic.

C. move the sheet away from the pole with uniform velocity if it is conducting.

D. move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar.

Choose the correct statement(s) from the options given below:

[NEET 2024]

A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as \(4\pi \times {10}^{-7}\mathrm{SI}\) units):

A \(2\) amp current is flowing through two small circular copper coils having radii ratio \(1:2\). The ratio of their respective magnetic moments will be

A \(2\) amp current is flowing through two small circular copper coils having radii ratio \(1:2\). The ratio of their respective magnetic moments will be

A 100-turn closely wound circular coil of radius 5 cm has a magnetic field of \(3.14\times {10}^{-3}T\) at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively :
(Take \({\mu }_{0}=4\pi \times {10}^{-7}Tm/A\))

A small circular loop of conducting wire has radius a and carries current \(I\). It is placed in a uniform magnetic field \(B\) perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period \(T\). If the mass of the loop is \(m\) then:

A uniform conducting wire of length \(12a\) and resistance ' \(R\) ' is wound up as a current carrying coil in the shape of,
(i) an equilateral triangle of side ' \(a\) '.
(ii) a square of side a'.
The magnetic dipole moments of the coil in each case respectively are:

The magnetic field vector of an electromagnetic wave is given by \(B={B}_{0}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\cos (kz-\omega t)\) where \(\hat{i},\hat{j}\) represents unit vector along x and y-axis respectively. At t = 0s, two electric charges \({q}_{1}\) of \(4\pi\) coulomb and \({q}_{2}\) of \(2\pi\) coulomb located at \(\left(0,0,\frac{\pi }{k}\right)\) and \(\left(0,0,\frac{3\pi }{k}\right)\) respectively, have the same velocity of \(0.5c\hat{i}\) (where c is the velocity of light). The ratio of the force acting on charge \({q}_{1}\) to \({q}_{2}\) is :

A long solenoid of \( 50 \mathrm{~cm} \) length having 100 turns carries a current of \( 2.5 \mathrm{~A} \). The magnetic field at the centre of the solenoid is \( \left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} \mathrm{~A}^{-1}\right) \)

[NEET 2020]

For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10mA is passed through it. If the torsional constant of the suspension wire is \(4.0\times {10}^{-5}\)Nm rad^–1, the magnetic field is 0.01T and the number of turns in the coil is 200, the area of each turn (in \({\mathrm{cm}}^{2}\) ) is:

Magnetic fields at two points on the axis of a circular coil at a distance of \(\ 0.05 \mathrm{~m} \) and 0.2 \(\ \mathrm{m} \) from the centre are in the ratio \(\ 8: 1\). The radius of coil is:

A solenoid is \(2\mathrm{m}\) long and \(3\mathrm{cm}\) in diameter. It has \(5\) layers of winding of \(1000\) turns each and carries a current of \(5\mathrm{A}\). What is the magnetic field at its centre? Use the standard value of \({\mu }_{0}\).

A square loop of area \(25{\mathrm{cm}}^{2}\) has a resistance of \(10\Omega\). The square loop is placed in a uniform magnetic field of magnitude \(40.0\mathrm{T}\). The plane of the loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in \(1.0\sec\), will be

[JEE Main 2023, 29 Jan (Shift 2)]

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.
A. The electron will experience magnetic force along the axis of the solenoid.
B. The electron will not experience magnetic force.
C. The electron will continue to move along the axis of the solenoid.
D. The electron will be accelerated along the axis of the solenoid.
E. The electron will follow parabolic path-inside the solenoid.

Choose the correct answer from the options given below:

A proton moving with a velocity \(3 \times 10^5 \mathrm{~m} / \mathrm{s}\) enters a magnetic field of \(0.3\) tesla at an angle of \(30^{\circ}\) with the field. The radius of curvature of its path will be (e/m for proton \(=10^8 \mathrm{C} / \mathrm{kg}\) )

A uniform conducting wire of length \(12a\) and resistance ' \(R\) ' is wound up as a current carrying coil in the shape of,
(i) an equilateral triangle of side ' \(a\) '.
(ii) a square of side a'.
The magnetic dipole moments of the coil in each case respectively are:

[NEET 2021]

An electron is moving along the positive x-axis. If the uniform magnetic field is applied parallel to the negative z-axis. then
A. The electron will experience magnetic force along positive y-axis
B. The electron will experience magnetic force along negative y-axis
C. The electron will not experience any force in magnetic field

D. The electron will continue to move along the positive x-axis
E. The electron will move along circular path in magnetic field

Choose the correct answer from the options given below:

[JEE Main 2023, 13 Apr (Shift 2)]

A wire carrying a current \(I\) along the positive \(\mathrm{x}\)-axis has length \(L\). It is kept in a magnetic field \(\vec{\mathrm{B}}=\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-4\hat{\mathrm{k}}\right)\mathrm{T}\). The magnitude of the magnetic force acting on the wire is :

A wire carrying a current \(I\) along the positive \(\mathrm{x}\)-axis has length \(L\). It is kept in a magnetic field \(\vec{\mathrm{B}}=\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-4\hat{\mathrm{k}}\right)\mathrm{T}\). The magnitude of the magnetic force acting on the wire is :

[NEET 2023]