Electric fields and charges practice · Medium

The electric field near a conducting surface having a uniform surface charge density $\sigma$ is given by

n identical mercury droplets charged to the same potential $V$ coalesce to form a single bigger drop. The potential of new drop will be

Two identical small conducting spheres having unequal positive charges $q_1$ and $q_2$ are separated by a distance $r$. If they are now made to touch each other and then separated again to the same distance, the electrostatic force between them in this case will be

A soap bubble of radius $R$ has uniformly distributed charge $Q$ on it's surface. It's energy is the self-energy of charges & surface energy due to surface tension. In equilibrium, this energy is minimum. Surface tension is $\mathrm{S}$. At equilibrium radius of bubble is R & pressure inside is $\mathrm{P}$. Pressure outside is $\mathrm{P}_0$. Then

Two point charges $+Q$ and $+q$ are separated by a certain distance. If $+Q > +q$ then in between the charges the electric field is zero at a point:

Assertion:- Electric field inside conductor is zero in electrostatics.
Reason:- Charge appears on surface of conductor.

Assertion (A): Electric lines of force cross each other.
Reason (R): The resultant electric field at a point is the superimposition of the electric fields at that point.

Assertion: A charged particle free to move in an electric field always moves along an electric field line

Reason: The electric field lines diverge from a negative charge and converge at a positive charge.

Two positive point charges are $3 \mathrm{~m}$ apart and their combined charge is $20 \mu \mathrm{C}$. If the force between them is $0.075 \mathrm{~N}$, then the charges are:

Assertion (A): When bodies are charged through friction, there is transfer of charge from one body to another. No charge is created or destroyed.
Reason (R): This is according to the law of conservation of electric charge.

A particle of mass $\text{m}$ and charge $\text{q}$ is thrown perpendicular to an electric field of intensity $\text{E}$ with an initial velocity $\text{v}.$ The particle moves a distance $x$ perpendicular to the field and a distance $\text{y}$ along the direction of the field. If $\text{y}=\alpha \text{x}^2$ then the $\alpha$ is given by:

Two concentric conducting thin shells of radius $r$ and $2 r$ carry charges $+2 q$ and $+6 q$, respectively. The magnitude of electric field at a distance $x$ outside and inside from the surface of outer sphere is same, then the volume of $x$ is

Assertion: If there exists coulomb attraction between two bodies, both of them must be charged.
Reason: In coulomb attraction two bodies are positively charged.

A conductor has been given a charge $- 3 \times {10^{ - 7}}C$ by transferring electron. Mass increase (in $kg$) of the conductor and the number of electron added to the conductor are respectively

Which of the following is correct regarding electric charge?
(i) If a body is having positive charge, then there is shortage of electrons.
(ii) If a body is having negative charge, then there is excess of electrons.
(iii) Minimum possible charge $= \pm 1.6 \times 10^{-19} \mathrm{C}$.
(iv) Charge is quantised, i.e. $Q= \pm n e$, where $n=1,2,3,4, \ldots$

Assertion : Total flux through a closed surface is zero if no charge is enclosed by the surface.

Reason : Gauss law is true for any closed surface, no matter what its shape or size is.

Assertion:- Two charged particles at rest experiences only electrical force.
Reason:- Charges at rest can only produce electric field.

Assertion: A charged conductor may have charged particle inside it.

Reason: There can't exist electric field lines inside the conductor.

How much positive and negative charge is there in a cup of water ?

In finding the electric field using Gauss law the formula $\left| E \right| = \frac{{{q_{\mathrm{enc}}}}}{{{\varepsilon _0}\left| A \right|}}$ is applicable. In the formula, ${\varepsilon _0}$ is permittivity of free space, $A$ is the area of Gaussian surface and ${q_{\mathrm{enc}}}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

A free pith-ball $A$ of $8 \mathrm{~g}$ carries a positive charge of $5 \times 10^{-8} \mathrm{C}$. What must be the nature and magnitude of charge that should be given to a second pith-ball $B$ fixed $5 \mathrm{~cm}$ below the former ball so that the upper ball is stationary?

Radius of a hollow sphere is $R$ and a charge $q$ is placed at the centre of hollow sphere. If the radius of sphere becomes half and charge also becomes half, then the value of emergent total flux from the surface of sphere is

A electric dipole is placed at an angle of $45^\circ$ to a non – uniform electric field. The dipole will experience

A solid ball of radius $R$ has a charge density $\rho$ given by $\rho=\rho_0\left(1-\frac{r}{R}\right)$ for $0 \leq r \leq R$. The electric field cutside the ball is

A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density$\rho = k\;{r^a}$, where $k$ and $a$ are constants and $r$ is the distance from its centre. If the electric field at $r = \frac{R}{2}$ is $\frac{1}{8}$ times that at $r = R,$ find the value of $a$

Statement-1: There is an isolated system of two charged conducting spheres $A$ and $B$. The resultant electric field at point $P$ is the sum of electric field at $P$ due to charged sphere $A$ only (that is, assuming sphere $B$ and all its effects to be absent) and the electric field at $P$ only due to sphere $B$ (that is, assuming sphere $A$ and all its effects to be absent).
Statement-2: Superposition theorem for electric field due to point charges states that resultant electric field at a point due to point charges is the sum of electric field at that point due to individual charges.

Two points are at distances $\mathrm{a}$ and $\mathrm{b}(\mathrm{a}<\mathrm{b})$ from a long string of charge per unit length $\lambda$. The potential difference between the points is proportional to -

Dielectric constant for metal is

The charge present in a doubly ionized helium atom is

Three equal charges are placed on the three corners of a square. If the force between ${q_1}$ and ${q_2}$ is ${F_{12}}$ and that between&nbsp; ${q_1}$ and ${q_3}$ is ${F_{13}}$, the ratio of magnitudes $\frac{{{F_{12}}}}{{{F_{13}}}}$ is