Desciption of Force

Q. An electron flies into a homogeneous magnetic field perpendicular to the lines of force. The velocity of electron is $4\times {10}^{7}m{s}^{-1}$ and induction of field is ${10}^{-3}$T. The tangential and normal accelerations of electron are

1. $7\times {10}^{15}m{s}^{-2},0$
2. $5\times {10}^{15}m{s}^{-2},0$
3. $3\times {10}^{15}m{s}^{-2},0$
4. $0,7\times {10}^{15}m{s}^{-2}$

Q. A charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $\overrightarrow{E}$ and $\overrightarrow{B}$ , with a velocity $\overrightarrow{v}$ perpendicular to both $\overrightarrow{E}$ and $\overrightarrow{B}$, and comes out without any change in magnitude or direction of $\overrightarrow{v}$. Then

1. $\overrightarrow{v}=\frac{\overrightarrow{E}\times \overrightarrow{B}}{B^2}$
2. $\overrightarrow{v}=\frac{\overrightarrow{E}\times \overrightarrow{E}}{B^2}$
3. $\overrightarrow{v}=\frac{\overrightarrow{E}\times \overrightarrow{B}}{E^2}$
4. $\overrightarrow{v}=\frac{\overrightarrow{B}\times \overrightarrow{B}}{E^2}$

Q. A charged particle goes undeflected in a region of space containing an electric field $\overrightarrow{E}$ and a magnetic field of intensity $\overrightarrow{B}$. Which of the following is possible?

1. $\overrightarrow{E}$ is parallel to $\overrightarrow{B}$ but $\overrightarrow{v}$ is perpendicular to $\overrightarrow{E}$
2. $\overrightarrow{E}$ is parallel to $\overrightarrow{B}$ and $\overrightarrow{v}$ parallel to $\overrightarrow{E}$
3. $\overrightarrow{E}$ is perpendicular to $\overrightarrow{B}$ and $\overrightarrow{v}$ is parallel to $\overrightarrow{E}\times \overrightarrow{B}$
4. $\overrightarrow{E}$ is perpendicualar to $\overrightarrow{B}$ and $\overrightarrow{v}$ is parallel to $\overrightarrow{E}.\overrightarrow{B}$

Q. A non-relativistic positive charge particle of charge $q$ and mass $m$ is projected perpendicular to uniform magnetic field $B$ as shown. Neglecting gravity, calculate $x-$coordinate of point on screen at which the charge particle will hit : $d=\frac{R\sqrt{3}}{2}$, where $R=\frac{mV}{qB}$

1. $\sqrt{3}R$
2. $2R$
3. The particle describes a helical path of radius $R=\frac{mv\sin \alpha }{qB}$
4. The particle describes a circular path of radius $R=\frac{mv}{qB}$

Q. A hollow conducting sphere of radius $R$ and total charge $q$ rotates about its diametrical axis with constant angular speed $\omega$. The magnitude of magnetic moment of the sphere is :

1. $\frac{2}{3}q{R}^2\omega$
2. $\frac{2}{5}q{R}^2\omega$
3. $\frac{1}{5}q{R}^2\omega$
4. $\frac{1}{3}q{R}^2\omega$

Q. A non-relativistic positive charge particle of charge $q$ and mass $m$ is projected perpendicular to uniform magnetic field $B$ as shown. Neglecting gravity, calculate $x-$coordinate of point on screen at which the charge particle will hit : $d=\frac{R\sqrt{3}}{2}$, where $R=\frac{mV}{qB}$

1. $\sqrt{3}R$
2. $2R$
3. The particle describes a helical path of radius $R=\frac{mv\sin \alpha }{qB}$
4. The particle describes a circular path of radius $R=\frac{mv}{qB}$

Q. A charged particle goes undeflected in a region of space containing an electric field $\overrightarrow{E}$ and a magnetic field of intensity $\overrightarrow{B}$. Which of the following is possible?

1. $\overrightarrow{E}$ is parallel to $\overrightarrow{B}$ but $\overrightarrow{v}$ is perpendicular to $\overrightarrow{E}$
2. $\overrightarrow{E}$ is parallel to $\overrightarrow{B}$ and $\overrightarrow{v}$ parallel to $\overrightarrow{E}$
3. $\overrightarrow{E}$ is perpendicular to $\overrightarrow{B}$ and $\overrightarrow{v}$ is parallel to $\overrightarrow{E}\times \overrightarrow{B}$
4. $\overrightarrow{E}$ is perpendicualar to $\overrightarrow{B}$ and $\overrightarrow{v}$ is parallel to $\overrightarrow{E}.\overrightarrow{B}$

Q. A non-relativistic positive charge particle of charge $q$ and mass $m$ is projected perpendicular to uniform magnetic field $B$ as shown. Neglecting gravity, calculate $x-$coordinate of point on screen at which the charge particle will hit : $d=\frac{R\sqrt{3}}{2}$, where $R=\frac{mV}{qB}$

1. $\sqrt{3}R$
2. $2R$
3. The particle describes a helical path of radius $R=\frac{mv\sin \alpha }{qB}$
4. The particle describes a circular path of radius $R=\frac{mv}{qB}$

Q. The two rails of a railway track, insulated from each other, and the ground, are connected to a millivoltmeter. What is the reading of the voltmeter when a train travels at a speed of 18 km $h^{-1}$ along the track? Given vertical component of earth's magnetic field = $0.2\times {10}^{-4}$ T and the separation between the rails = 1 m.

1. 1 mV
2. 3 mV
3. 6 mV
4. 9 mV

Q. A proton of mass m and charge +e is moving in a circular orbit of a magnetic field with energy 1MeV. What should be the energy of $\alpha$ -particle (mass = 4 m and charge = +2e), so that it can revolve in the path of same radius?

1. 1 MeV​
2. 4 MeV​
3. 2 MeV​
4. 0.5 MeV​

Q.

A 2 MeV proton is moving perpendicular to a uniform magnetic field of 2.5 tesla. The force on the proton is

1. $2.5\times {10}^{-10}N$

2. $7.6\times {10}^{-11}N$

3. $2.5\times {10}^{-11}N$

4. $7.6\times {10}^{-12}N$