Circular Kinematics

Q.

An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to _________.

Q.

What is the trajectory of an electron when it moves perpendicular to the electric field is

Q. A proton and an $\alpha$- particle enter a uniform magnetic field perpendicularly with the same speed. If proton takes $25\mu sec$ to make 5 revolutions, then the periodic time for the $\alpha$ - particle would be

1. $25\mu sec$.
2. $50\mu sec$.
3. $10\mu sec$.
4. $5\mu sec$.

Q. Which one of the following pattern of electrostatic lines of force is not possible?

1. 
2. 
3. 
4. 

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. 
2. 
3. 
4. 

Q. The magnetic force is acting on a charged particle of charge $-2\mu C$ in a magnetic field of $2$ $T$ which is in $y$ direction. When the particle velocity is$\left(2\hat{i}+3\hat{j}\right)\times {10}^{6}m/s$, then the force acting on the particle will be

1. $4$ $N$in $z$ direction
2. $8$ $N$in $y$ direction
3. $8$ $N$in $z$ direction
4. $8$ $N$ in $-z$ direction

Q. The surface charge densities of two thin concentric spherical shells are $\sigma$ and $-\sigma$ respectively as shown in the figure. Their radii are $R$ and $2R$. Now they are connected by a thin wire. Potential on either of the shell will be.

1. $-\frac{3\sigma R}{2{\epsilon }_{\circ }}$
2. $-\frac{2\sigma R}{3{\epsilon }_{\circ }}$
3. $-\frac{\sigma R}{2{\epsilon }_{\circ }}$
4. zero

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 proton, a deuteron and an $\alpha$- particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $r_p,r_d$ and $r_{\alpha }$ denote respectively the radii of the trajectories of these particles, then

1. 
2. 
3. 
4. 

Q.

A proton with 1 MeV kinetic energy is moving in a circular path of radius R in a uniform magnetic field. What should be the energy of an α - particle to describe a circle of same radius in the same magnetic field?

1. 4 MeV

2. 2 MeV

3. 1 MeV

4. 0.5 MeV

Q.

A proton and an $\alpha -$particle, having kinetic energies $K_p$ and $K_{\alpha }$ respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that $\alpha -$particle is $2:1$. The ratio of $K_p:K_{\alpha }$ is :

1. $1:8$

2. $1:4$

3. $8:1$

4. $4:1$

Q.

A Proton and an Alpha particle are accelerated through the same potential difference enter in a region of uniform magnetic field with their velocities perpendicular to the field they also have same Kinetic energy. compare the radii of circular path followed by them

Q.

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

1. $2:1:1and4:2:1$

2. $1:2:4and2:1:1$

3. $1:2:4and1:1:2$

4. $4:2:1and2:1:1$

Q. 23.) A particle having a mass of 10-2 kg carries a chargeof 5 x 10-8C. The particle is given an initialhorizontal velocity of 105 ms-1 in the presence ofelectric field E and magnetic field B. To keep theparticle moving in a horizontal direction, it isnecessary that(a) B should be perpendicular to the direction ofvelocity and E should be along the direction ofvelocity(b) Both B and E should be along the direction ofvelocity(c) Both B and are mutually perpendicular andperpendicular to the direction of velocityB should be along the direction of velocity andE should be perpendicular to the direction ofvelocity(d)Which one of the following pairs of statements ispossible?(1) (a) and (c)(3) (b) and (c)AIPMT (Mains)-2010\rbrack(2) (c) and (d)(4) (b) and (d)

Q. An electron, a proton, a deuteron and an alpha particle, each having the same speed are in a magnetic field perpendicular to the direction of the velocities of the particles. The radius of the circular orbits of these particles are respectively $R_e,R_p,R_d$ and $R_{\alpha }$. It follows that

1. $R_e=2R_p$
2. $R_p=R_d$
3. $R_d=R_{\alpha }$
4. $R_p=R_{\alpha }$

Q. Two identical particles having the same mass $m$ and charges $+q$ and $-q$, separated by a distance $d$, enter in a uniform magnetic field $B$ directed perpendicular to paper inward with speeds $v_1$ and $v_2$ as shown in the figure. The particles will not collide if

1. $d>\frac{m}{Bq}(v_1+v_2)$
2. $d>\frac{m}{Bq}(v_1+v_2)$
3. $d>\frac{2m}{Bq}(v_1+v_2)$
4. $v_1=v_2$

Q. When a charged particle circulates in a normal magnetic field, then the area of its circulation is proportional to

1. its charge
2. its momentum
3. its kinetic energy
4. Magnetic fields intensity

Q. An electron of mass $m$ is accelerated through a potential difference of $V$ and then it enters a magnetic field of induction $B$ normal to the lines. Then, the radius of the circular path is

1. $\sqrt{\frac{2eV}{m}}$
2. $\sqrt{\frac{2Vm}{e{B}^2}}$
3. $\sqrt{\frac{2Vm}{eB}}$
4. $\sqrt{\frac{2Vm}{e^{2}B}}$

Q. An electron and a proton enter a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is true?

1. Trajectory of electron is less curved
2. Trajectory of proton is less curved
3. Both move on straight line path
4. Both trajectories are equally curved

Q. An electron and a proton with equal momentum enter perpendicularly into a uniform magnetic field, then

1. The path of proton shall be less curved than that of electron
2. Path of both will be straight line
3. The path of proton shall be more curved than that of electron
4. Both are equally curved

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. 3 cm
4. 2.35 cm

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

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

Q. Correct curve of potential $\left(V\right)$ versus distance $\left(r\right)$ from centre of two charged spherical shells is

1. 
2. 
3. 
4. 

Q. A charged particle of charge $q$ and mass $m$ is moving with velocity $v$ (as shown in the figure) in a uniform magnetic field B along negative z – direction. Select the correct alternative(s).

1. Velocity of the particle when it comes out from the magnetic field is $\overrightarrow{v}=v\cos {60}^{\circ }\widehat{+}v\sin {60}^{\circ }\hat{j}$
2. Time for which the particle was in magnetic field is $\frac{\pi m}{3qB}$
3. Distance travelled in magnetic field is $\frac{\pi mv}{3qB}$
4. None of these

Q. A charge $Q$ is distributed over three concentric spherical shells of radii $a,b,c(a<b<c)$ such that their surface charge densities are equal to one another. The total potential at a point at distance $r$ from their common centre, where $r<a$, would be

1. $\frac{Q}{12\pi {ϵ}_0}\frac{ab+bc+ca}{abc}$
2. $\frac{Q(a^2+b^2+c^2)}{4\pi {ϵ}_0(a^3+b^3+c^3)}$
3. $\frac{Q(a+b+c)}{4\pi {ϵ}_0(a^2+b^2+c^2)}$
4. $\frac{Q}{4\pi {ϵ}_0(a+b+c)}$

Q. A proton is projected with a velocity ${10}^{7}m/s$ at right angle to a uniform magnetic field of induction 100 mT. The time taken by proton to traverse ${90}^{\circ }$ arc is

1. $0.8\times {10}^{-7}s$
2. $1.57\times {10}^{-7}s$
3. $2.43\times {10}^{-7}s$
4. $3.24\times {10}^{-7}s$

Q. An electron (mass = $9\times {10}^{-31}kg,$ charge $=1.6\times {10}^{-19}$ C ) whose kinetic energy is $7.2\times {10}^{-20}$ J is moving in a circular orbit in a magnetic field of $9\times {10}^{-5}weber/m^2$. The radius of the orbit is

1. 1.25 cm
2. 2.5 cm
3. 25.0 cm
4. 12.5 cm

Q. If the intensity of magnetic field at a point on the axis of a current carrying coil of radius $R$ is half of that at the centre of the coil, then the distance of that point from the centre of the coil will be

1. $\frac{R}{2}$
2. $R\sqrt{2^{\left(\frac{1}{3}\right)}-1}$
3. $\frac{3R}{2}$
   
4. $R\sqrt{4^{\left(\frac{1}{3}\right)}-1}$

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.

Doubly ionized helium ions are projected with a speed of $10km{s}^{-1}$ in a direction perpendicular to a uniform magnetic field of magnitude 1.0 T. Find (a) the force acting on an ion, (b) the radius of the circle in which it circulates and (c) the time taken by an ion to complete the circle.