Velocity Selector

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. 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. 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 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. 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. 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. 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 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. 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 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. ${10}^{16}Wb/m^2$.