Electric fields and charges practice · Mixed difficulty

Two charges placed in air repel each other by a force of ${10^{ - 4}}N.$ When oil is introduced between the charges, the force becomes $2.5 \times {10^{ - 5}}N.$ The dielectric constant of oil is

Statement-1: Any net charge of a conductor resides on its outer surface.
Statement-2: The electrostatic energy of a conductor is minimum when charge is spread over the surface.

While taking off synthetic clothes, seeing a spark or
hearing a crackle, are due to

Assertion: Two identicalballs are charged by $q$. They are suspended from a common point by two insulating threads $l$ each. In equilibrium the angle between the threads is $180^{\circ}$. (Ignore gravity)

Reason: In equllibrium tension in the springs is $T=\frac{1}{4 \pi \varepsilon_0} \times \frac{q \cdot q}{l^2}$

Assertion:- An electric charge is fixed in free space which produces an electric field around it. No work is done in displacing another charge from its position to any other position.
Reason:- Electrostatic field is non conservative.

Two charges of $5\,\,\mu c$ and $- 45\,\,\mu c$ are separated by a distance of 42 cm. Electrostatic field strength from the smaller charge is zero at a distance of

Estimate the number of electrons in $100 \mathrm{~g}$ of water. How much is the total negative charge on these electrons?

A dipole has two charges $+1 \mu {C}$ and $-1 \mu C$ and each have mass $1 {~kg}$. The separation between the charges is $1 {~m}$. An electric field $20 \times 10^3 {v} / {m}$ is applied on the dipole. If the dipole is deflected through $2^{\circ}$ from the equilibrium position, time taken by it to come to the equilibrium position again is

Assertion:- Electrostatic energy does not follow superposition principle.
Reason:-Electrostatic energy density is a quadratic function.

Assertion:- When a positive point charge is placed near a neutral conductor then the Latter becomes negatively charged.
Reason:- Induction is possible in conductors only.

Assertion(A): If a bob of a simple pendulum is kept in a horizontal electric field, its period of oscillation will remain same.

Reason(R): If bob is charged and kept in horizontal electric field, then the time period will be decreased.

Assertion: Electric lines of force cross each other.

Reason: Electric field at a point superimposes to give one resultant electric field.

Two equal and opposite charges are placed at points $P$ and $Q.$ The null point on the line joining them is

An infinite line charge produces a field of $18 \times 10^4 \mathrm{~N} / \mathrm{C}$ at $0.02 \mathrm{~m}$. The linear charge density is

The bob of simple pendulum is hanging vertically down from a fixed identical bob by means of string of length $l$. If both bobs are charged with a charge with a charge $q$ each, time period of the pendulum is (ignore the radii of the bobs)

Gauss’s law of electrostatics would be invalid if

A force of $4N$ is acting between two charges in air if the space between them is completely filled with glass $\left( {{\varepsilon _r} = 8} \right)$, then the new force will be …… $N$

In a region, the intensity of an electric field is given by $E=8 \hat{i}+8 \hat{j}+\hat{k}$ in $\mathrm{NC}^{-1}.$ The electric flux through a surface $S=10 \hat{i} m^2$ in the region is

Assertion: A charge particle is released from rest in magnetic field then it will move in circular path.
Reason: Work done by magnetic field is non zero.

Electric charges under action of electric forces is called

A hollow metallic sphere of radius $10\;cm$ is given a charge of $3.2 \times {10^{ - 9}}$ $C$.The electric intensity at a point $4\;cm$ from the centre is

Assertion:- For a charged shell, potential inside shell depends only on the field inside shell.
Reason:- Potential of shell may be determined only by the field outside.

The magnitude of the average electric field normally present in the atmosphere just above the surface of the earth is about $150\,N/C,$ directed inward towards the center of the earth. This gives the total net surface charge carried by the earth to be: $\left[ {{\text{Given}}\,{\varepsilon _0} = 8.85 \times {{10}^{ - 12}}\,{C^2}/N - {m^2},\,{R_E} = 6.37 \times {{10}^6}\,m} \right]$

Electric lines of force:

An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius $r.$ The coulomb force ${\vec F}$ between the two is 

The repulsive force between two equal charges $(Q)$ is $F.$ To reduce force by 25% how much charge is transferred from first to second:-

Two charges $+1 \mu \mathrm{C}$ and $+4 \mu \mathrm{C}$ are situated at a distance in air. The ratio of the forces acting on them is

Assertion:- Net charge density inside a conductor is zero.
Reason:- Equal and opposite charges are present in conductor.

Which of the following is the correct statement of Gauss law for electrostatics in a region of charge distribution in free space?

Two masses $M_1$ and $M_2$ carry positive charges $Q_1$ and $Q_2$, respectively. They are dropped to the floor in a laboratory setup from the same height where there is a constant electric field vertically upwards. $M_1$ hits the floor before $M_2$. Then,