Circular Kinematics

Q. A particle with a specific charge $s$ is fired with a speed $v$ towards a wall at a distance $d$ perpendicular to the wall. What minimum magnetic field must exist in this region for the particle to not to hit the wall?

1. $\frac{v}{sd}$
2. $\frac{2v}{sd}$
3. $\frac{v}{2sd}$
4. $\frac{v}{4s}$

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

1. Magnetic field
2. Charge
3. Mass of the particle
4. Velocity of the particle

Q. A particle carrying a charge $q$, moves with a constant angular speed $\omega$ on a circular path. The radius of this path is $r$ & center is at origin, how many times does the magnetic field become zero at point $(2r,4r)$

1. 1 time
2. 2 times
3. Never
4. 3 times

Q. A charged particle moves in a uniform magnetic field perpendicular to it, with a radius of curvature $4cm$. On passing through a metallic sheet, it loses half of its kinetic energy. Then, the radius of curvature of the particle is

1. $2cm$
2. $4cm$
3. $8cm$
4. $2\sqrt{2}cm$

Q. The figure shows a set of equipotential surfaces. There are a few points marked on them. An electron is being moved from one point to other. Which of the following statement is/are correct?

1. As the electron moves from $E$ to $A$, the potential energy increases.
2. Work done by the electric field, in moving the electron from $C$ to $D$ is same as from $D$ to $E$.
3. The electric field is directed along +$x$ -axis.
4. Work done by the electric field, in moving the electron from $B$ to $C$, is positive.

Q. An electron of mass $9.0\times {10}^{-31}\text{kg}$ under the action of a magnetic field moves in a circle of radius $2\text{cm}$ at a speed of $3\times {10}^6\text{m/s}$. If a proton of mass $1.8\times {10}^{-27}\text{kg}$ has to move in a circle of same radius and in the same magnetic field, then its speed must be

Q. Two particles A and B of masses $m_A$ and $m_B$ respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are $v_A$ and $v_B$ respectively, and the trajectories are as shown in the figure. Then

1. $m_A{v}_A<m_B{v}_B$
2. $m_A{v}_A>m_B{v}_B$
3. $m_A<m_B$ and $v_A<v_B$
4. $m_A=m_B$ and $v_A=v_B$

Q. An electron enters with its velocity in the direction of the uniform electric lines of force. Consider lines of force to be straight. Then

1. The path of the electron will be a circle
2. The path of the electron will be a parabola
3. The magnitude of velocity of the electron will first decrease and then increase
4. The magnitude of velocity of the electron will first increase and then decrease

Q. A particle of mass $m$ and charge $q$ enters with velocity $v_0$ perpendicular to a magnetic field B (coming out of the plane of the paper) as shown in the figure. It moves in the magnetic field for time $t=\frac{\pi m}{4qB}$, and then enters into a constant electric field region. The electric and magnetic fields are present only in a rectangular region of thickness $d$. The length of rectangular region is $l$. The particle enters parallel to and grazing the side $RQ$ and leaves the region at $P$.
Given : $v_0=(\sqrt{2}+1)m{s}^{-1}$.
$\frac{E}{B}=8m{s}^{-1},l=\left|\frac{4\sqrt{2}}{5}{v}_0\right|$ metres and $\frac{m}{qB}=\frac{4}{5}$

Displacement of the particle in x-direction before it enters in the electric field is

1. $\frac{3}{5}(2+\frac{1}{\sqrt{2}})m$
2. $\frac{4}{5}(1+\frac{1}{\sqrt{2}})m$
3. $\frac{4}{5}(1-\frac{3}{\sqrt{2}})m$
4. None of these

Q. A particle of mass $m$ and charge $q$ enters with velocity $v_0$ perpendicular to a magnetic field B (coming out of the plane of the paper) as shown in the figure. It moves in the magnetic field for time $t=\frac{\pi m}{4qB}$, and then enters into a constant electric field region. The electric and magnetic fields are present only in a rectangular region of thickness $d$. The length of rectangular region is $l$. The particle enters parallel to and grazing the side $RQ$ and leaves the region at $P$.
Given : $v_0=(\sqrt{2}+1)m{s}^{-1}$.
$\frac{E}{B}=8m{s}^{-1},l=\left|\frac{4\sqrt{2}}{5}{v}_0\right|$ metres and $\frac{m}{qB}=\frac{4}{5}$

Displacement of the particle in x-direction before it enters in the electric field is

1. $\frac{3}{5}(2+\frac{1}{\sqrt{2}})m$
2. $\frac{4}{5}(1+\frac{1}{\sqrt{2}})m$
3. $\frac{4}{5}(1-\frac{3}{\sqrt{2}})m$
4. None of these

Q. Four charge particles $H{e}^{++}$, proton, deutron and $L{i}^{++}$ enters a region of uniform magnetic field and moves in a circular path of different radius. List I gives above four particles while list II gives magnitude of some quantity.

$\begin{array}{cc}\text{List I}& \text{List II}\\ \text{I -}H{e}^{++}& \text{P)}1\\ \text{II -}\text{Proton}& \text{Q)}2\\ \text{III -}\text{deutron}& \text{R)}\frac{1}{\sqrt{2}}\\ \text{IV)}L{i}^{++}& \text{S)}\sqrt{2}\\ & \text{T)}\frac{\sqrt{7}}{2}\\ & \text{U)}\frac{1}{2}\end{array}$
If kinetic energy of all four particles is same than correct match for radius of four particles in units of radius of proton is

1. $I-P,II-P,III-S,IV\to T$
2. $I\to Q,II-P,III-S,IV\to T$
3. $I\to S,II-P,III-S,IV-T$
4. $I-R,II-P,III-S,IV-T$

Q. Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius $R_1$ and $R_2$ respectively. The ratio of mass of X to that of Y is

1. ${\left(\frac{R_1}{R_2}\right)}^{1/2}$
2. $\frac{R_2}{R_1}$
3. ${\left(\frac{R_1}{R_2}\right)}^2$
4. $\frac{R_1}{R_2}$

Q. A particle of charge $q$ and mass $m$ moves rectilinearly under the action of an electric field, $E=4-2x$, where $x$ is a distance from the point where the particle was initially at rest. Calculate the distance travelled by the particle till it comes to rest.

1. $3\text{m}$
2. $1\text{m}$
3. $4\text{m}$
4. $2\text{m}$

Q. A proton and a deutron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field B. For motion of proton and deutron on circular path of radius $R_p$ and $R_d$ respectively, the correct statement is

1. $R_d=\sqrt{2}{R}_p$
2. $R_d=\frac{R_p}{\sqrt{2}}$
3. $R_d=R_p$
4. $R_d=2R_p$

Q. A charge (q, m) perpendicularly enters a semi - infinite B - field with a speed v. Find the deviation and the time it spends in the B-field.

1. $\frac{\pi }{2},\frac{\pi m}{2qB}$
2. $\pi ,\frac{\pi m}{qB}$
3. $2\pi ,\frac{2\pi m}{qB}$
4. $\frac{\pi }{4},\frac{\pi m}{qB}$

Q. Electrons move at right angle to a magnetic field of $1.5\times {10}^{-2}$ Tesla with a speed of $6\times {10}^7$ m/s. If the specific charge of the electron is $1.7\times {10}^{11}$ C/kg, then the radius of the circular path will be?

1. 2.9 cm
2. 3.9 cm
3. 2.35 cm
4. 3 cm

Q. A proton and an $\alpha$ particle enter a uniform magnetic field with same speed as shown in figure.

1. Both the particles will follow same circular path in clockwise manner.
2. Both the particles will stay for same time in the field.
3. $\alpha$ particle will stay for more time in the field than proton.
4. Radius of the path of proton is more than the radius of path of $\alpha$ - particle.

Q. A proton and an $\alpha$ particle enter a uniform magnetic field with same velocity, then ratio of the radii of path describe by them will be?

1. 1 : 2
2. 1 : 1
3. 2 : 1
4. None of these

Q. A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region x > b is

1. qbB/m
2. q(b – a)B/m
3. qaB/m
4. q(b+a)B/2m