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Given below are two statements:
Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.
Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.
In the light of the above statements, choose the most appropriate answer from the options given below:

An electron with energy \( 0.1 \,\text{keV} \) moves at right angle to the earth’s magnetic field of \( 1\times 10^{-4}\, \text{Wb m}^{-2} \). The frequency of revolution of the electron will be (Take mass of electron \( =9.0\times 10^{-31}\,\text{kg} \))

A proton, a deuteron and an \( \alpha \)- particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is:

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \( r_{d} \) and \( r_{p} \) are the radii of their circular paths respectively, then the ratio \( \frac{r_{d}}{r_{p}} \) will be \( \sqrt{x} : 1 \) where \( x \) is ________.

A closely wounded circular coil of radius \( 5 \, \text{cm} \) produces a magnetic field of \( 37.68 \times 10^{-4} \, \text{T} \) at its center. The current through the coil is __________ \( \text{A} \).
[Given, number of turns in the coil is \( 100 \) and \( \pi = 3.14 \) ]

A wire \( X \) of length \( 50\,\text{cm} \) carrying a current of \( 2\,\text{A} \) is placed parallel to a long wire \( Y \) of length \( 5\,\text{m} \). The wire \( Y \) carries a current of \( 3\,\text{A} \). The distance between two wires is \( 5\,\text{cm} \) and currents flow in the same direction. The force acting on the wire \( Y \) is

A beam of light travelling along \( X \)-axis is described by the electric field \( E_{y} = 900 \sin \omega (t - x/c) \). The ratio of electric force to magnetic force on a charge \( q \) moving along \( Y \)-axis with a speed of \( 3 \times 10^{7} \ \text{m s}^{-1} \) will be:
(Given speed of light \( = 3 \times 10^{8} \ \text{m s}^{-1} \))

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to \( 4 \) times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle:

The current sensitivity of a galvanometer can be increased by:
(a) decreasing the number of turns
(b) increasing the magnetic field
(c) decreasing the area of the coil
(d) decreasing the torsional constant of the spring
Choose the most appropriate answer form the options given below:

Two long current carrying conductors are placed parallel to each other at a distance of \( 8 \ \text{cm} \) between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is \( 300 \ \mu \text{T} \). The equal current flowing in the two conductors is:

A long straight wire with a circular cross-section having radius \( R \), is carrying a steady current \( I \). The current \( I \) is uniformly distributed across this cross-section. Then the variation of magnetic field due to current \( I \) with distance \( r \) (\( r<R \)) from its centre will be:

A long solenoid carrying a current produces a magnetic field \( B \) along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to:

Two long parallel conductors \( S_1 \) and \( S_2 \) are separated by a distance \( 10 \, \text{cm} \) and carrying currents of \( 4 \, \text{A} \) and \( 2 \, \text{A} \) respectively. The conductors are placed along x-axis in X-Y plane. There is a point \( P \) located between the conductors (as shown in figure). A charge particle of \( 3\pi \) coulomb is passing through the point \( P \) with velocity \( \vec{v} = (2 \hat{i} + 3 \hat{j}) \, \text{m/s} \); where \( \hat{i} \) & \( \hat{j} \) represents unit vector along \( x \) & \( y \) axis respectively. The force acting on the charge particle is \( 4 \pi \times 10^{-5} \, (-x \hat{i} + 2 \hat{j}) \, \text{N} \). The value of \( x \) is:

The magnetic field at the centre of a circular coil of radius \( r \), due to current \( I \) flowing through it, is \( B \). The magnetic field at a point along the axis at a distance \( \frac{r}{2} \) from the centre

As shown in the figure, a metallic rod of linear density \( 0.45 \, \text{kg} \, \text{m}^{-1} \) is lying horizontally on a smooth inclined plane which makes an angle of \( 45^\circ \) with the horizontal. The minimum current flowing in the rod required to keep it stationary, when \( 0.15 \, \text{T} \) magnetic field is acting on it in the vertical upward direction, will be:
{Use \( g = 10 \, \text{m/s}^2 \)}

\( B_X \) and \( B_Y \) are the magnetic field at the centre of two coils \( X \) and \( Y \) respectively each carrying equal current. If coil \( X \) has \( 200 \) turns and \( 20 \, \text{cm} \) radius and coil \( Y \) has \( 400 \) turns and \( 20 \, \text{cm} \) radius, the ratio of \( B_X \) and \( B_Y \) is:

The electric current in a circular coil of \( 2 \) turns produces a magnetic induction \( B_1 \) at its centre. The coil is unwound and is rewound into a circular coil of \( 5 \) turns and the same current produces a magnetic induction \( B_2 \) at its centre. The ratio of \( \dfrac{B_2}{B_1} \) is:

A wire of length \( 314 \, \text{cm} \) carrying current of \( 14 \text{A} \) is bent to form a circle. The magnetic moment of the coil is __________ \( \text{A}\!\!-\!\!\text{m}^2 \). [Given \( \pi = 3.14 \) ]

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In an uniform magnetic field, speed and energy remains the same for a moving charged particle.
Reason (R): Moving charged particle experiences magnetic force perpendicular to its direction of motion.

Two charged particles, having same kinetic energy are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is \( 6 : 5 \) and their respective masses ratio is \( 9 : 4 \). Then, the ratio of their charges will be :

Two concentric circular loops of radii \( r_1 = 30\,\text{cm} \) and \( r_2 = 50\,\text{cm} \) are placed in X–Y plane as shown in the figure. A current \( I = 7\,\text{A} \) is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately:

A triangular shaped wire carrying \( 10 \, \text{A} \) current is placed in a uniform magnetic field of \( 0.5 \, \text{T} \), as shown in figure. The magnetic force on segment \( CD \) is:
(Given \( BC = CD = BD = 5 \, \text{cm} \))

An infinitely long hollow conducting cylinder with radius \( R \) carries a uniform current along its surface. Choose the correct representation of magnetic field \( (B) \) as a function of radial distance \( (r) \) from the axis of cylinder.

Two \( 10 \, \text{cm} \) long, straight wires, each carrying a current of \( 5 \, \text{A} \) are kept parallel to each other. If each wire experienced a force of \( 10^{-5} \, \text{N} \), then separation between the wires is _______ \( \text{cm} \).

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is:

A single ionized magnesium atom \( (A = 20) \) ion is accelerated to kinetic energy \( 5 \, \text{keV} \), and is projected perpendicularly into a magnetic field \( B \) of the magnitude \( 0.5 \, \text{T} \). The radius of path formed will be _____ \( \text{cm} \).

A velocity selector consists of electric field \( \vec{E} = E\,\hat{k} \) and magnetic field \( \vec{B} = B\,\hat{\jmath} \) with \( B = 12\,\text{mT} \). The value of \( E \) required for an electron of energy \( 728\,\text{eV} \) moving along the positive x-axis to pass undeflected is:

A charge particle is moving in a uniform magnetic field \( (2\hat{i} + 3\hat{j}) \, \text{T} \). If it has an acceleration of \( (\alpha \hat{i} - 4\hat{j}) \, \text{m}/\text{s}^2 \), then the value of \( \alpha \) will be:

The magnetic field at the centre 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 centre on its axis is \( B_2 \). The value of \( {B_1}/{B_2} \) will be:

Two parallel, long wires are kept \( 0.20 \, \text{m} \) apart in vacuum, each carrying current of \( x \, \text{A} \) in the same direction. If the force of attraction per meter of each wire is \( 2 \times 10^{-6} \, \text{N} \), then the value of \( x \) is approximately:

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JEE Main 2022 24th June Morning Shift

The magnetic field at the centre of a circular coil of radius \( r \), due to current \( I \) flowing through it, is \( B \). The magnetic field at a point along the axis at a distance \( \frac{r}{2} \) from the centre