Velocity Selector

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