Moving Charge in a Magnetic Field

When an electron is kept in a strong magnetic field, then

Lorentz magnetic force is acting on a particle of charge $q$ moving with velocity $\vec{V}$ in magnetic field $\vec{B}$. The work done by this force on the charged particle is

A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of solenoid. If $g$ is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy:

The charged particle moving in a uniform magnetic field of $(3\hat{i} + 2\hat{j})\text{ T}$ has an acceleration $\left(4\hat{i} - \frac{x}{2}\hat{j}\right)\text{ m/s}^2$. The value of $x$ is

A charged particle of mass $m$ and charge $q$ travels on a circular path, (of radius $5$ unit) is perpendicular to a magnetic field $B$. The time taken by a particle to complete $10$ revolutions is

A charge moves in a circular path perpendicular to a magnetic field. The time period of revolution is independent of

In the cyclotron, as radius of the circular path of the charged particle increases, ($\omega$ = angular velocity, V = linear velocity)

1 μC charge moving with velocity $\vec{v} = (\hat{i} - 2\hat{j} + 3\hat{k})$ m/s in the region of magnetic field $\vec{B} = (2\hat{i} + 3\hat{j} - 5\hat{k})$ T. The magnitude of force acting on it is $\sqrt{\alpha} \times 10^{-6}$ N. The value of $\alpha$ is _______.

Two particles X and Y of masses '$m_1$' and '$m_2$' respectively, having equal charges after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii '$r_1$ ' and '$r_2$' respectively. The ratio of '$r_1$' and '$r_2$' is

A charged particle is moving in a uniform magnetic field in a circular path of radius 'R'. When the energy of the particle becomes 3 times the original, the new radius will be

A charged particle $q$ is accelerated by a potential difference of $V$ enters a region of uniform magnetic field of induction $B$ at right angles to the direction of the field. The charged particle completes semi circle of the radius $r$ inside the magnetic field. The mass of the charged particle is (all quantities are in SI units)

A 5 mg particle carrying a charge of $5\pi \times 10^{-6}\text{ C}$ is moving with velocity of $(3\hat{i} + 2\hat{k}) \times 10^{-2}\text{ m/s}$ in a region having magnetic field $\vec{B} = 0.1\hat{k}\text{ Wb/m}^2$. It moves a distance of $\alpha$ meter along $\hat{k}$ when it completes 5 revolutions. The value of $\alpha$ is ______。

A particle having charge $10^{-9}$ C moving in $x\text{-}y$ plane in fields of $0.4\hat{j}$ N/C and $4 \times 10^{-3}\hat{k}$ T experiences a force of $(4\hat{i} + 2\hat{j}) \times 10^{-10}$ N. The velocity of the particle at that instant is _________ m/s.

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v} = \left(\frac{v_0}{\sqrt{2}}\hat{x} + \frac{v_0}{\sqrt{2}}\hat{y}\right)$. There exists a uniform magnetic field $\vec{B} = B_0\hat{z}$ and a space varying electric field $\vec{E} = E_0 e^{-\lambda x}\hat{x}$ within the region $0 \leqslant x \leqslant L$. After travelling a distance such that $x$-coordinate has changed from $x = 0$ to $x = L$, the change in the kinetic energy is ______.

Lorentz magnetic force is acting on a particle of charge q moving with velocity $\vec{V}$ in a magnetic field $\vec{B}$. The work done by this force on the charged particle is

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.

Reason (R): The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below:

A particle of charge $1.6\ \mu\text{C}$ and mass $16\ \mu\text{g}$ is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is _________ s. $(\pi = 3.14)$

A particle of charge $q$ moves with a velocity $\vec{V} = a\hat{i}$ in a magnetic field $\vec{B} = b\hat{j} + c\hat{k}$, where ' $a$ ', ' b ' and ' c ' are constants. The magnitude of force experienced by particle is

A particle of charge $q$, mass $m$ and kinetic energy $E$ enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of $r$ with $E$?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Assertion A: If Oxygen ion $(\text{O}^{-2})$ and Hydrogen ion $(\text{H}^{+})$enter normal to the magnetic field with equal momentum, then the path of $\text{O}^{-2}$ ion has a smaller curvature than that of $\text{H}^{+}$. Reason R: A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.

In the light of the above statements, choose the correct answer from the options given below

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

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2 \times 10^{5}\text{ ms}^{-1}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x \times 10^{4}\text{ N/C}$. The value of $x$ is _________. Take the mass of the proton $= 1.6 \times 10^{-27}\text{ kg}$.

Consider a long thin conducting wire carrying a uniform current I. A particle having mass " $m$ " and charge " $q$ " is released at a distance " $a$ " from the wire with a speed $v_0$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance $x$ from the wire. The value of $x$ is [ $\mu_0$ is vacuum permeability]

Bohr model is applied to a particle of mass m and charge $q$ is moving in a plane under the influence of a transverse magnetic field (B). The energy of the charged particle in the second level will be ( $h =$ Planck's constant)

Uniform magnetic fields of different strengths $(B_1$ and $B_2)$, both normal to the plane of the paper exist as shown in the figure. A charged particle of mass $m$ and charge $q$, at the interface at an instant, moves into the region 2 with velocity $v$ and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?

(Consider the velocity of the particle to be normal to the magnetic field and $B_2 > B_1$)

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is:

A charged particle is moving along a magnetic field line. What is the magnetic force acting on the particle? $\left(\sin 0^\circ = 0, \sin\frac{\pi}{2} = 1\right)$

The electrostatic force $\left(\vec{F}_1\right)$ and magnetic force $\left(\vec{F}_2\right)$ acting on a charge $q$ moving with velocity $v$ can be written:

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then:

A charge of $4.0\ \mu\text{C}$ is moving with a velocity of $4.0 \times 10^{6}\text{ ms}^{-1}$ along the positive $y$ axis under a magnetic field $\vec{B}$ of strength $(2\hat{k})\text{ T}$. The force acting on the charge is $x\hat{i}N$. The value of $x$ is __________.

Cyclotron is used to

An electron moves through a uniform magnetic field $\vec{B} = B_0\hat{i} + 2B_0\hat{j}\text{ T}$. At a particular instant of time, the velocity of electron is $\vec{u} = 3\hat{i} + 5\hat{j}\text{ m/s}$. If the magnetic force acting on electron is $\vec{F} = 5e\hat{k}\text{ N}$, where $e$ is the charge of electron, then the value of $B_0$ is _________ $T$.

A charged particle is moving in a uniform magnetic field in a circular path of radius ' $R$ '. When the kinetic energy of the particle is increased to three times, then the new radius will be

Electron of mass ' $m$ ' and charge ' $q$ ' is travelling with speed ' $v$ ' along a circular path of radius ' $R$ ' at right angles to a uniform magnetic field of intensity ' B '. If the speed of the electron is halved and the magnetic field is doubled, the resulting path would have radius

A charged particle of charge ' $q$ ' is accelerated by a potential difference ' $V$ ' enters a region of uniform magnetic field ' $B$ ' at right angles to the direction of field. The charged particle completes semicircle of radius ' $r$ ' inside magnetic field. The mass of the charged particle is

A charged particle is moving in a uniform magnetic field in a circular path with radius ' $R$ '. When the energy of the particle is doubled, then the new radius will be

A proton and a deuteron $(q = +e, m = 2.0\text{u})$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deuteron path to the radius $r_p$ of the proton path is:

Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $X$ and $Y$ is:

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec{E}$ and $\vec{B}$ represent the electric and magnetic fields respectively, then the region of space may have:

(A) $E = 0,\ B = 0$

(B) $E = 0,\ B \neq 0$

(C) $E \neq 0,\ B = 0$

(D) $E \neq 0,\ B \neq 0$

Choose the most appropriate answer from the options given below:

An electron with kinetic energy $5\text{ eV}$ enters a region of uniform magnetic field of 3 $\mu\text{T}$ perpendicular to its direction. An electric field $E$ is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is __________ $\text{NC}^{-1}$. (Given, mass of electron $= 9 \times 10^{-31}\text{ kg}$, electric charge $= 1.6 \times 10^{-19}\text{ C}$)

An electron is projected along the axis of circular conductor carrying current I. Electron will experience

An electron is moving along the positive $\mathrm{x}$-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 $\mathrm{x}$-axis

E. The electron will move along circular path in magnetic field

Choose the correct answer from the options given below:

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 charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron:

Electron of mass '$m$' and charge '$q$' is travelling with speed '$v$' along a circular path of radius '$R$', at right angles to a uniform magnetic field of intensity '$B$'. If the speed of the electron is halved and the magnetic field is doubled, the resulting path would have radius

A charge particle of $2\ \mu\text{C}$ accelerated by a potential difference of $100\text{ V}$ enters a region of uniform magnetic field of magnitude $4\text{ mT}$ at right angle to the direction of field. The charge particle completes semicircle of radius $3\text{ cm}$ inside magnetic field. The mass of the charge particle is __________ $\times 10^{-18}\text{ kg}$

A proton with a kinetic energy of $2.0\text{ eV}$ moves into a region of uniform magnetic field of magnitude $\frac{\pi}{2} \times 10^{-3}\text{ T}$. The angle between the direction of magnetic field and velocity of proton is $60^\circ$. The pitch of the helical path taken by the proton is __________ $\text{cm}$. (Take, mass of proton $= 1.6 \times 10^{-27}\text{ kg}$ and Charge on proton $= 1.6 \times 10^{-19}\text{ C}$ ).

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:

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.

An electron and a proton having the same momenta enter perpendicularly into a magnetic field. What are their trajectories in the field?

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:

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 deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If rd and rp 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 charge particle is moving in a uniform magnetic field $(2\hat{i} + 3\hat{j})\text{ T}$. If it has an acceleration of $(\alpha\hat{i} - 4\hat{j})\text{ m/s}^2$, then the value of $\alpha$ will be:

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:

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 singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be _____________ cm.

A velocity selector consists of electric field $\vec{E} = E\hat{k}$ and magnetic field $\vec{B} = B\hat{j}$ 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:

(Given, mass of electron $= 9.1 \times 10^{-31}\text{ kg}$)

A cyclotron is used to accelerate protons. If the operating magnetic field is $1.0\text{ T}$ and the radius of the cyclotron 'dees' is $60\text{ cm}$, the kinetic energy of the accelerated protons in MeV will be: $[\text{use } m_p = 1.6 \times 10^{-27}\text{ kg}, e = 1.6 \times 10^{-19}\text{ C}$ ]

A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be:

(Take: e = 1.6 $\times$ 10$-$19 C, mp = 1.67 $\times$ 10$-$27 kg)

Two long parallel conductors S1 and S2 are separated by a distance 10 cm and carrying currents of 4A and 2A 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 charged particle of 3$\pi$ coulomb is passing through the point P with velocity$\vec{v} = (2\hat{i} + 3\hat{j})$ m/s; where $\hat{i}$ and $\hat{j}$ represents unit vector along x & y axis respectively.

The force acting on the charged particle is $4\pi \times 10^{-5}(-x\hat{i} + 2\hat{j})$ N. The value of x is:

An electron is projected along the axis of circular conductor carrying current '$\mathrm{I}$' The electron will experience

A charge Q is moving $\overrightarrow{dl}$ distance in the magnetic field $\vec{B}$. Find the value of work done by $\vec{B}$.

Two ions having same mass have charges in the ratio 1: 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2: 3. The ratio of the radii of their circular trajectories is:

A charge moves with velocity '$V$' through electric field $(E)$ as well as magnetic field (B). then the force acting on it is

An infinitely long straight conductor carries a current of 5A as shown. An electron is moving with a speed of 105 m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then:

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let rd and r$\alpha$ be their respective radii of circular path. The value of $\frac{r_d}{r_\alpha}$ is equal to:

A proton and an $\alpha$-particle, having kinetic energies Kp and K$\alpha$ respectively, enter into a magnetic field at right angles.

The ratio of the radii of trajectory of proton to that of $\alpha$-particle is 2: 1. The ratio of Kp: K$\alpha$ is:

A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _________ and their speed is _______, in the ratio.

If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolutions made by a proton in a cyclotron to achieve one sixth of the speed of light is ...............

[mp = 1.67 $\times$ 10$-$27 kg, e = 1.6 $\times$ 10$-$19 C, Speed of light = 3 $\times$ 108 m/s]

A charge $q$ moves with velocity $v$ through electric field $\mathrm{E}$ as well as magnetic field (B). Then, the force acting on it is

A charged particle carrying charge 1 $\mu$C is moving

with velocity $\left(2\hat{i} + 3\hat{j} + 4\hat{k}\right)$ ms–1. If an external

magnetic field of $\left(5\hat{i} + 3\hat{j} - 6\hat{k}\right)$ × 10–3 T exists in the region where the particle is moving then the force on the particle is $\vec{F}$× 10–9 N. The vector $\vec{F}$is:

Proton with kinetic energy of 1MeV moves from south to north. It gets an acceleration of 1012 m/s2 by an applied magnetic field (west to east). The value of magnetic field: (Rest mass of proton is 1.6 × 10–27 kg):

An $\alpha$-particle of energy 10 eV is moving in a circular path in uniform magnetic field. The energy of proton moving in the same path and same magnetic field will be [mass of $\alpha$-particle $= 4$ times mass of proton]

A charged particle is moving in a uniform magnetic field in a circular path of radius $R$. When the energy of the particle becomes three times the original, the new radius will be

The figure shows a region of length ‘l’ with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 $\times$ 105 ms–1 making an angle 60° with the field. If the proton completes 10 revolution by the time it cross the region shown, ‘l’ is close to

(mass of proton = 1.67 $\times$ 10–27 kg, charge of the proton = 1.6 $\times$ 10–19 C)

A beam of protons with speed 4 × 105 ms–1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton = 1.67 $\times$ 10–27 kg, charge

of the proton = 1.69 $\times$ 10–19 C)

An electron is moving along +x direction with a velocity of 6 $\times$ 106 ms–1. It enters a region of uniform electric field of 300 V/cm pointing along +y direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the x direction will be:

A particle of charge q and mass m is moving with a velocity $-v\hat{i}$ (v $\neq$ 0) towards a large screen placed in the Y - Z plane at a distance d. If there is a magnetic field $\vec{B} = B_0\hat{k}$, the maximum value of v for which the particle will not hit the screen is:

An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a current I. The electron gun shoots an electron along the radius of the solenoid with speed v. If the electron does not hit the surface of the solenoid, maximum possible value of v is (all symbols have their standard meaning):

A charged particle of mass 'm' and charge 'q' moving under the influence of uniform electric field $E\hat{i}$ and a uniform magnetic field $B\hat{k}$follows a trajectory from point P to Q as shown in figure. The velocities at P and Q are respectively, $v\hat{i}$and $-2v\hat{j}$. Then which of the following statements (A, B, C, D) are correct?

(Trajectory shown is schematic and not to scale):

(A) E = $\frac{3}{4}\left(\frac{mv^2}{qa}\right)$

(B) Rate of work done by the electric field at P is $\frac{3}{4}\left(\frac{mv^3}{a}\right)$

(C) Rate of work done by both the fields at Q is zero

(D) The difference between the magnitude of angular momentum of the particle at P and Q is 2mav.

A particle of mass m and charge q has an initial velocity$\vec{v} = v_0\hat{j}$. If an electric field $\vec{E} = E_0\hat{i}$ and magnetic field $\vec{B} = B_0\hat{i}$ act on the particle, its speed will double after a time:

Ionized hydrogen atoms and $\alpha$-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths rH: r$\alpha$ will be:

Maximum kinetic energy gained by the charged particle in the cyclotron is independent of

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicualr to the plane. Let rp, re and rHe be their respective radii, then

A proton and an $\alpha$-particle (with their masses in the ratio of 1: 4 and charges in the ratio of 1: 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp: r$\alpha$ of the circular paths described by them will be;

In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 $\times$ 10–19 C Mass of the electron = 9.1 $\times$ 10–31 kg]

A particle of mass m and charge q is in an electric and magnetic field given by

$\vec{E} = 2\hat{i} + 3\hat{j};\ \vec{B} = 4\hat{j} + 6\hat{k}.$