Electric fields and charges practice · Mixed difficulty

Four metal conductors having different shapes
 I. A sphere 
 II. Cylinder
 III. Pear
 IV. Lightning conductor
 are mounted on insulating stands and charged. The one which is best suited to retain the charges for a longer time is

The electric field at a distance $2 \mathrm{~cm}$ from the centre of a hollow spherical conducting shell of radius $4 \mathrm{~cm}$ having a charge of $2 \times 10^{-3} \mathrm{Con}$ its surface is

A body is negatively charged means

Which of the following statements is/are correct?
I. For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
II. The electrical potential of a sphere of radius $R$ with charge $Q$ uniformly distributed on the surface is given by $\frac{Q}{4 \pi \varepsilon_0 R}$.
III. Work done in carrying a point charge from one point to another in an electrostatic field depends on the path along which the point charge is carried.

A charge $q$ is placed on a solid metallic object of irregular shape. Charge $q$ will distribute itself.

A positively charged insulator is brought near (but does not touch) two metallic sphere that are in contact. The metallic spheres are then separated. The sphere which was initially farthest from the insulator will have:

A charge $\text{q}$ is fixed. Another charge $\text{Q}$ is brought near it and rotated in a circle of radius $\text{r}$ around it. Work done during rotation is

Regarding a semiconductor which one of the following statements is wrong?

Suppose a rod is given a negative charge by
rubbing it with wool. Which one of the
following statements is correct in this case?

A surface $S=10 \hat{{j}}$ is kept in an electric field ${E}=2 \hat{{i}}+4 \hat{{j}}+7 \hat{{k}}$. How much electric flux will come out through this surface?

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

Assertion: The potential difference between any two points in an electric field depends only on initial and final position.

Reason: Electric field is a conservative field so the work done per unit positive charge does not depend on path followed.

An electric dipole placed in a non-uniform electric field experiences

Assertion: The property that the force with which two charges attract or repel each other are not affected by the presence of a third charge.

Reason: Force on any charge due to a number of other charge is the vector sum of all the forces on that charge due to other charges, taken one at a time.

Given below are two statements:
Statement I An electric diploe is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.
Statement II If $R$ is the radius of a solid metallic sphere and $Q$ be the total charge on it. The electric field at any point on the spherical surface of radius $r( < R)$ is zero but the electric flux passing through this closed spherical surface of radius $r$ is not zero.
In the light of the above statements, choose the correct answer from the options given below.

Assertion: Coulomb force and gravitational force follow the same inverse-square law.
Reason: Both laws are same in all aspects.

In charging by induction,

The force of repulsion between two electrons at a certain distance is $2 F$. The force between two protons separated by the same distance is: $\left(m_p=1836\right.\left.{m}_e\right)$

Electric field line at the surface of equipotential surface is

If a charged particle $(+q, m)$ is projected along $+x$ direction with initial velocity $u$ and an uniform electric field exist in space along ($-$ve) $y$-direction then path of partcile is (neglect gravity)

Choose the incorrect statement.

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: