Lorentz Force

A particle of mass $\mathrm{m}$, carrying charge $\mathrm{q}$ is accelerated through a potential of $\mathrm{V}\left(\mathrm{Volt}\right)$. When this accelerated charge comes under the influence of perpendicular magnetic field, the force acting on it is:

The period of revolution of a charged particle inside a cyclotron does not depend on:

Which of the following is the correct expression of the velocity selector?

A particle having mass $m$ and charge $q$ is released from the origin in a region in which electric field and magnetic field are given by
$\overrightarrow{B}=-B_0\overrightarrow{j}\text{ and }\overrightarrow{E}=E_0\overrightarrow{k}$.
Find the speed of the particle as a function of its $z-$coordinate.

Describe the working of cyclotron. Draw the diagram showing path of particle in both "Dees" Derive expression for frequency of cyclotron.

In the given figure, an electron moves at speed $v=100 \mathrm{m} {\mathrm{s}}^{-1}$ along an $\mathrm{x}$-axis, through uniform electric and magnetic fields. The magnetic field is directed into the page and has magnitude $5.00 \mathrm{T}$. In unit-vector notation, what is the electric field?

If instead of electron a neutron enters a field, what will be its direction of motion? Give reasons for your answer.

(a)A monoenergetic electron beam with electron speed of $5.20\times {10}^6 \mathrm{m}/\mathrm{s}$ is subject to a magnetic field of $1.30\times {10}^{-4} \mathrm{T}$ normal to the beam velocity. What is the radius of the circle traced by the beam, given $\raisebox{1ex}{$e$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$ for electron equals $1.76\times {10}^{11} {\mathrm{CKg}}^{-1}$.

(b)Is the formula you employ in (a) valid for calculating radius of the path of a $20 \mathrm{MeV}$ electron beam? If not, in what way is it modified?

Answer the following question:
Interstellar space has an extremely weak magnetic field of the order of ${10}^{-12} \mathrm{T}$. Can such a weak field be of any significant consequence? Explain.

A magnetic field set up using Helmholtz coils is uniform in a small region and has a magnitude of $0.75 \mathrm{T}$. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through $15 \mathrm{kV}$ enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is $9\times {10}^{-5} \mathrm{V}{\mathrm{m}}^{-1}$, make a simple guess as to what the beam contains. Why is the answer not unique?

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?

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?

In a certain region of space, electric field $\overrightarrow{\mathrm{E}}$ and magnetic field $\overrightarrow{\mathrm{B}}$ are perpendicular to each other and an electron enters in the region perpendicular to the direction of $\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{E}}$ both and moves undeviated, then velocity of electron is -

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

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be, 

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its

If an electron and a proton having the same momentum enter perpendicular to a magnetic field, then_____.