Motion of Charges in an Electric Field

An electric charge of magnitude '$2e$' and mass '$2m$' is moving in an electric field 'E'. The acceleration imparted to the charge is

A simple pendulum has a bob with mass $m$ and charge $q$. The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec{E}$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ______.

Two metal plates (A, B) are kept horizontally with separation of $\left(\frac{12}{\pi}\right)$ cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 g/cm3) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials VA and VB are required on plates A and B respectively in order to ensure the droplets do not descend. The values of VA and VB are ______.

(Neglect the air resistance to the droplets and take g = 10 m/s2)

A charged particle of mass ' $m$ ' and charge ' $q$ ' is at rest. It is acce:lerated in a uniform electric field of intensity ' $E$ ': for time ' $t$ '. The kinetic energy of the particles after time $t$ is

A small bob of mass 100 mg and charge $+10\,\mu\text{C}$ is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density ' $\sigma$ ' as shown in figure. If string subtends an angle of $45^\circ$ with the sheet at equilibrium the charge density of sheet will be. (Given, $\epsilon_0 = 8.85 \times 10^{-12}\,\frac{\text{F}}{\text{m}}$ and acceleration due to gravity, $g = 10\,\frac{\text{m}}{\text{s}^2}$)

A particle of mass ' $m$ ' and charge ' $q$ ' is fastened to one end ' $A$ ' of a massless string having equilibrium length $l$, whose other end is fixed at point ' $O$ '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the $x$-axis is

A particle ' $A$ ' has charge ' $+q$ ' and a particle ' $B$ ' has charge ' $+4q$ '. Each has same mass ' $m$ '. When they are allowed to fall from rest through the same potential, the ratio of their speeds will become (particle A to particle B)

An electron of mass ' $m$ ' and charge ' $q$ ' is accelerated from rest in a uniform electric field of intensity ' $E$ '. The velocity acquired by it as it travels a distance ' $l$ ' is ' $v$ '. The ratio $\frac{q}{m}$ in terms of $E, l$ and $v$ is

A small particle carrying a negative charge of $1.6 \times 10^{-19}\text{ C}$ is suspended in equilibrium between two horizontal metal plates 8 cm apart having a potential difference of 980 V across them. The mass of the particle is $\left[g = 9.8\text{ m/s}^2\right]$

An infinitely long positively charged straight thread has a linear charge density $\lambda\text{ C m}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is:

A particle of charge '$-q$' and mass '$m$' moves in a circle of radius '$r$' around an infinitely long line charge of linear charge density '$+\lambda$'. Then time period will be given as:

(Consider $k$ as Coulomb's constant)

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$ having surface charge density $+\sigma$. The electron at $t = 0$ is at a distance of $1\text{ m}$ from $S$ and has a speed of $1\text{ m/s}$. The maximum value of $\sigma$ if the electron strikes $S$ at $t = 1\text{ s}$ is $\alpha\left[\frac{m\epsilon_0}{e}\right]\frac{C}{m^2}$, the value of $\alpha$ is ___________.

Suppose a uniformly charged wall provides a uniform electric field of $2 \times 10^{4}\text{ N/C}$ normally. A charged particle of mass $2\text{ g}$ being suspended through a silk thread of length $20\text{ cm}$ and remain stayed at a distance of $10\text{ cm}$ from the wall.

Then the charge on the particle will be $\frac{1}{\sqrt{x}}\,\mu\text{C}$ where $x =$ ___________. [use $g = 10\text{ m/s}^2$ ]

An electron of mass '$m$' and charge '$q$' is accelerated from rest in a uniform electric field of strength '$E$'. The velocity acquired by the electron, when it travels a distance '$L$', is

An electron revolves around an infinite cylindrical wire having uniform linear charge density $2 \times 10^{-8}\text{ C m}^{-1}$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ___________ $\times 10^{6}\text{ m s}^{-1}$. Given mass of electron $= 9 \times 10^{-31}\text{ kg}$

A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($\theta$) of deviation of the path of electron as it comes out of the field is ___________ (in degree).

A stream of positively charged particles having $\frac{q}{m} = 2 \times 10^{11}\,\frac{C}{kg}$ and velocity$\vec{v}_0 = 3 \times 10^{7}\hat{i}\text{ m/s}$ is deflected by an electric field $1.8\hat{j}$ kV/m. The electric field exists in a region of 10 cm along $x$ direction. Due to the electric field, the deflection of the charged particles in the $y$ direction is _________ mm.

The bob of a simple pendulum of length '$L$' has a mass '$m$' and charge '$q$'. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. The period of oscillations of the simple pendulum is (acceleration due to gravity $g > qE/m$)

A vertical electric field of magnitude 4.9 $\times$ 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be:

(Given: g = 9.8 m/s2)

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 $\times$ 105 NC${}^{-1}$. If the charge on the particle is 40 $\mu$C and the initial velocity is 200 ms${}^{-1}$, how much distance it will travel before coming to the rest momentarily:

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is:

A uniform electric field $E = (8\,m/e)\text{ V/m}$ is created between two parallel plates of length $1\text{ m}$ as shown in figure, (where $m =$ mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of $2\text{ m/s}$. The angle of the deviation $(\theta)$ of the path of the electron as it comes out of the field will be _________.

Two identical positive charges $Q$ each are fixed at a distance of '2a' apart from each other. Another point charge $q_0$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_0$ executes $\text{SHM}$. The time period of oscillation of charge $q_0$ will be:

An electron of mass '$m$' and charge '$q$' is accelerated from rest in a uniform electric field of strength '$E$'. The velocity acquired by the electron when it travels a distance '$L$' is

Two particles $A$ and $B$ having same mass have charge $+q$ and $+4q$ respectively. When they are allowed to fall from rest through same electric potential difference, the ratio of their speeds '$V_A$' to '$V_B$' will become

A charge of magnitude '2e' and mass '4m' is moving in an electric field $\vec{E}$. The acceleration imparted to the above charge is

An oil drop of radius 2 mm with a density 3g cm${}^{-3}$ is held stationary under a constant electric field 3.55 $\times$ 105 V m${}^{-1}$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider g = 9.81 m/s2)

An inclined plane making an angle of 30$^\circ$ with the horizontal is placed in a uniform horizontal electric field $200\,\frac{N}{C}$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.

[g = 9.8 m/s2; $\sin 30^\circ = \frac{1}{2}$; $\cos 30^\circ = \frac{\sqrt{3}}{2}$]

Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: (m = mass of charged particle)

A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x << 1 m), the particle executes SHM. Its angular frequency of oscillation will be ____________ $\times$ 105 rad/s if q2 = 10 C2.

A body having specific charge 8 $\mu$C/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be _______________ s.

A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass?

(Curves are drawn schematically and are not to scale).

A charged particle (mass m and charge q)

moves along X-axis with velocity V0. When it

passes through the origin it enters a region having uniform electric field

$\vec{E} = -E\hat{j}$ which extends upto x = d.

Equation of path of electron in the region x > d is

A particle of charge q and mass m is subjected to an electric field

E = E0 (1 – $a$x2) in the x-direction, where $a$ and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

The bob of a simple pendulum has mass 2g and a charge of 5.0 μC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is: (take g = 10 m/s2)

An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is

A body of mass $M$ and charge $q$ is connected to spring of spring constant $k.$ It is oscillating along $x$-direction about its equilibrium position, taken to be at $x = 0,$ with an amplitude $A$. An electric field $E$ is applied along the $x$-direction. Which of the following statements is correct?

A uniform electric field $\vec{E}$ exists between the plates of a charged condenser. A charged particle enters the space between the plates and perpendicular to $\vec{E}$. The path of the particle between the plates is a:

A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of 25.5 kVm $-1$. The density of liquid is $1.26 \times 10^{3}$ kg m $-3$. The radius of the drop is (neglect buoyancy).

Two charges, each equals to $q,$ are kept at $x = -a$ and $x = a$ on the $x$-axis. A particle of mass $m$ and charge $q_0 = \frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y \ll a)$ along the $y$-axis, the net force acting on the particle is proportional to

Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2 - V_1 = 20\text{ V}.$ (i.e., plate $2$ is at a higher potential). The plates are separated by $d = 0.1\text{ m}$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1.$ What is its speed when it hits plate $2$?

$\left(e = 1.6 \times 10^{-19}\text{ C},\ m_e = 9.11 \times 10^{-31}\text{ kg}\right)$

A charged ball $B$ hangs from a silk thread $S,$ which makes angle $\theta$ with a large charged conducting sheet $P,$ as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to

A charged oil drop is suspended in a uniform field of $3 \times 10^{4}\text{ V/m}$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $= 9.9 \times 10^{-15}\text{ kg}$ and $g = 10\text{ m/s}^2$)

A particle of mass $m$ and charge $q$ is placed at rest in a uniform electric field $E$ and then released. The kinetic energy attained by the particle after moving a distance $y$ is