Velocity Selector

Q.

A helium nucleus makes a full rotation in a circle of radius $0.8$ meter in two second. The value of $B$ (magnetic field) at the center of the circle will be

Q. A particle of charge $-16\times {10}^{-18}$ coulomb moving with velocity 10 m/s along the x-axis enters a region where a magnetic field of induction B is along the y-axis, and an electric field of magnitude ${10}^{4}V/m$ is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is

1. ${10}^{-3}Wb/m^2$
2. ${10}^{3}Wb/m^2$
3. ${10}^{5}Wb/m^2$
4. ${10}^{16}Wb/m^2$.

Q.

An electron is moving along positive $x$ direction with a velocity of $6\times {10}^{6}m{s}^{-1}$. It enters a region of the uniform electric field of $300V/cm$ pointing along positive $y$ 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

1. $3\times {10}^{-4}T$, along $–z$ direction

2. $5\times {10}^{-3}T$, along $–z$ direction

3. $5\times {10}^{-3}T$, along $+z$ direction

4. $3\times {10}^{-4}T$, along $+z$ direction

Q. A bar magnet is oscillating in the earth's magnetic field with a period $T$. What happens to its period and motion if its mass is quadrupled ?

1. Motion remains $S.H.M$ with time period =$2T$
2. Motion remains $S.H.M$ with time period =$4T$
3. Motion remains $S.H.M$ with time period =$\frac{T}{2}$
4. Motion remains $S.H.M$ and period remains nearly constant.

Q. A particle having a charge of $10.0\mu C$ and mass $1\mu g$ moves in a circle of radius 10 cm under the influence of a magnetic field of induction 0.1T. When the particle is at a point P, a uniform electric field is switched on so that the particle starts moving along the tangent with a uniform velocity. The electric field is

1. 0.1 V/m
2. 1.0 V/m
3. 10.0 V/m
4. 100 V/m

Q.

What are the imitations of cyclotron.

Q. Answer the following questions: (a) A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle? (b) A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment? (c) An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.

Q. Consider the motion of a positive point charge in a region where there are simultanceous uniform electric and magnetic fields $\overrightarrow{E}=E_0\hat{j}$ and $\overrightarrow{B}=B_{)}\hat{j}$. At time $t=0$, this charge has velocity $\overrightarrow{v}$ in the $x-y$ plane, making an angle $\theta$ with the $x$-axis. Which of the following option(s) is/are correct for time $t>0$?

1. If $\theta =0^o$, the charge undergoes helical motion with contant pitch along the $y$-axis
2. If $\theta =0^o$, the charge moves in a circular path in the $x-z$ lane
3. If $\theta ={90}^o$, the charge undergoes linear but accelerated motion along the $y$-axis
4. If $\theta ={10}^o$, the charge undergoes helical motion with its pitch increasing with time, along the $y$-axis

Q. An electron moves along a straight line as shown inside a charged parallel plate capacitor. The space between the plates is filled with constant magnetic field of induction $\overrightarrow{B}$. Time taken for the straight line motion of the electron in the capacitor is

1. $\frac{e\sigma }{{\epsilon }_{0}lB}$
   
2. $\frac{{\epsilon }_{0}lB}{\sigma }$
   
3. $\frac{e\sigma }{{\epsilon }_{0}B}$
   
4. $\frac{{\epsilon }_{0}B}{e\sigma }$
   

Q.

Two particles X and Y having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii $r_1$‘ and ’$r_2$ respectively. The ratio of the mass of X to that of Y is:

Q. In Exercise 4.11 obtain the frequency of revolution of the electron inits circular orbit. Does the answer depend on the speed of the electron? Explain.

Q. If a charged particle of charge to mass ratio$\frac{q}{m}=\alpha$ is entering in a uniform magnetic field of strength $B$ which is extended up to $4d$ as shown in figure at a speed $v=\left(2\alpha dB\right)$
If the radius of the circular path described in the magnetic field is $nd$, find value of $n$.

Q. A block of mass m and charge q is released from rest on incline plane of angle $\theta$ and coefficient of friction $\mu$. $\theta$ is greater than angle of repose. A magnetic field perpendicular to page inwards also exist as shown in figure, then

1. Speed of block increases linearly.
2. Maximum speed attained by block is $\frac{mg}{\mu qB}(sin\theta -\mu cos\theta )$
3. Speed of block increases exponentially and reaches infinity
4. Time to reach maximum speed is infinity

Q. Answer the following questions: (a) Quarks inside protons and neutrons are thought to carryfractional charges [(+2/3)e ; (–1/3)e]. Why do they not show upin Millikan’s oil-drop experiment? (b) What is so special about the combination e/m? Why do we notsimply talk of e and m separately? (c) Why should gases be insulators at ordinary pressures and startconducting at very low pressures? (d) Every metal has a definite work function. Why do allphotoelectrons not come out with the same energy if incidentradiation is monochromatic? Why is there an energy distributionof photoelectrons? (e) The energy and momentum of an electron are related to thefrequency and wavelength of the associated matter wave by therelations:E = h ν, p = λhBut while the value of λ is physically significant, the value of ν(and therefore, the value of the phase speed ν λ) has no physicalsignificance. Why?

Q. A charged particle of specific charge $\alpha$ enters in a magnetic field $\overrightarrow{B}=\frac{B_0}{\sqrt{2}}(\hat{j}+\hat{k})$ with a velocity $\overrightarrow{v}=v_0\hat{i}$. Then (specific charge = charge per unit mass)

1. Path of the particle is a helix
2. Path of the particle is circle
3. Distance moved by the particle in time $t=\frac{\pi }{B_0\alpha }$ is $\frac{\pi v_0}{B_0\alpha }$
4. Velocity of the particle after time $t=\frac{\pi }{B_0\alpha }$ is $(\frac{v_0}{2}\hat{i}+\frac{v_0}{2}\hat{j})$

Q. Two blocks of masses $M_1$ and $M_2$ are connected with a string which passes over a smooth pulley. The mass $M_1$ is placed on a rough incline plane as shown in Fig. The coefficient of friction between the block and the inclined planes is $\mu$. What should be the minimum mass $M_2$ so that the block $M_1$ slides upwards?

1. $M_2=M_1(sin\theta +\mu cos\theta )$
2. $M_2=M_1(sin\theta -\mu cos\theta )$
3. $M_2=\frac{M_1}{sin\theta +\mu cos\theta }$
4. $M_2=\frac{M_1}{sin\theta -\mu cos\theta }$

Q. A particle having a charge of $10.0\mu C$ and mass $1\mu g$ moves in a circle of radius 10 cm under the influence of a magnetic field of induction 0.1T. When the particle is at a point P, a uniform electric field is switched on so that the particle starts moving along the tangent with a uniform velocity. The electric field is

1. 0.1 V/m
2. 1.0 V/m
3. 10.0 V/m
4. 100 V/m

Q. A body is moving down an inclined plane of slope ${37}^o$. The coefficient of friction between the body and the plane varies as $\mu =0.3x$, where $x$ is the distance traveled down the plane by the body. The body will have maximum speed at $(\sin {37}^o=\frac{3}{5})$.

1. at $x=2m$
2. at $x=1.16m$
3. at bottom most point of the plane
4. at $x=2.5m$

Q.

Comment on the corrections of the following two statements based on the given situation.

Consider a line of length ‘l’ and uniform charge density $\lambda$. Assume a Gaussian surface S, a cylinder of radius R and height h.

Statement 1: $\phi =fluxthroughS=\frac{\lambda H}{{ϵ}_0}$

Statement 2: $|\overrightarrow{E}|atallthepointsonitscurvedsurface=\frac{\lambda }{{ϵ}_{0}2\pi R}$

1. True, True

2. True, false

3. False, True

4. False, False

Q. An electron moves along a straight line as shown inside a charged parallel plate capacitor. The space between the plates is filled with constant magnetic field of induction $\overrightarrow{B}$. Time taken for the straight line motion of the electron in the capacitor is

1. $\frac{e\sigma }{{\epsilon }_{0}lB}$
   
2. $\frac{{\epsilon }_{0}lB}{\sigma }$
   
3. $\frac{e\sigma }{{\epsilon }_{0}B}$
   
4. $\frac{{\epsilon }_{0}B}{e\sigma }$
   

Q. A block is moving on an inclined plane making an angle ${45}^o$ with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is $3$ times the force required to just prevent it from sliding down. lf we define $N=10\mu$, then $N$ is

1. 3
2. 4
3. 5
4. 2

Q. A charge particle moves underacted in a region of crossed electric and magnetic fields. If the electric field is switched off, the particle has an initial acceleration $a$, if the magnetic field is switched off, instead of the electric field, the particle will have an initial acceleration:

1. equal to $0$
2. $>a$
3. equal to $a$
4. $<a$

Q.

The diagram given below is showing a radioactive source $R$ in a thick walled container having a narrow opening. The radiations pass through an electric field between plates C and D.

Consider the above diagram and complete it in order to show the paths of $\alpha$, $\beta$ and $\gamma$-radiations.

Q. If the direction of the initial velocity of the charged particle is perpendicular to the magnetic field, the orbit of charged particle will be

1. a straight line
2. a cycloid
3. a circle
4. a helix

Q. Imagine that you are seated in a room and there is a uniform magnetic field pointing vertically downwards in it . At the center of the room an electron is projected horizontally with a certain speed. The path of the electron in this field are:

1. electron moves in clockwise path
2. electron moves in anticlockwise path
3. electron moves left wards
4. electron moves right wards

Q. An electron moves straight inside a charged parallel plate capacitor of uniform surface charge density $\sigma$. The space between the plates is filled with constant magnetic field of induction $\overrightarrow{B}$. The time of straight line motion of the electron in the capacitor is:

1. $\frac{e\sigma }{{ϵ}_{0}lB}$
2. $\frac{{ϵ}_{0}lB}{\sigma }$
3. $\frac{e\sigma }{{ϵ}_{0}B}$
4. $\frac{{ϵ}_{0}B}{e\sigma }$

Q. A light ray falling at an angle of ${45}^0$ which the surface of a clean slab of ice of thickness 1.00 m is refracted into it at an angle of 30${}^0$. alculate the time taken by the light rays to cross the slab. Speed of light in the vacuum =3$\times {10}^8$ m/s${}^{-1}$