What is invariance of the electric charge?

Important Questions on Electric Charges and Fields

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

A point charge $+ Q$ is held at rest at a point $P.$ Another point charge $-q$ , whose mass is $m$ , moves at a constant speed $v$ in a circular orbit of radius $R_1$ around $P$. The work required to increase the radius of revolution of $-q$ from $R_1$, to another orbit $R_2$ is $\left(R_2>R_1\right)$ $\left(\text{where\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}K=\frac{1}{4\pi {\epsilon }_0}\right)$

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Two identical charged spheres suspended from a common point by two massless strings of lengths $l$, are initially at a distance $d\left(d\ll l\right)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $\mathrm{\upsilon }$. Then $\mathrm{\upsilon }$ varies as a function of the distance $x$ between the spheres, as

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Two positively charged spheres of masses $m_1 \text{and} m_2$ are suspended from a common point at the ceiling by identical insulating massless strings of length $l$ . Charges on the two spheres are $q_1 \text{and} q_2$, respectively. At equilibrium, both strings make the same angle $\theta$ with the vertical. Then

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

The radius of a nucleus is given by $r_0{A}^{1/3}$ where $r_0=1.3\times {10}^{-15} \mathrm{m}$ and $A$ is the mass number of the nucleus, the Lead nucleus has $A=206$, the electrostatic force between two protons in this nucleus is approximately

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

The charge present in a doubly ionized helium atom is

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Four identical pendulums are made by attaching a small ball of mass $100 \mathrm{g}$ on a $20 \mathrm{cm}$ long thread and suspended from the same point. Now each ball is given charge $q$ so that balls move away from each other with each thread making an angle of ${45}^{\mathrm{o}}$ from the vertical. The value of $q$ is close to $\left(\frac{1}{4{\mathrm{\pi \epsilon }}_0}=9\times {10}^9, \mathrm{S}.\mathrm{I}.\mathrm{ }\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}\right)$

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Two charges, each equal 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 $(y\ll \mathrm{a)}$ along the y-axis, the net force acting on the particle is proportional to :

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

A certain charge $2Q$ is divided at first into two parts $q_1$ and $q_2$. Later the charges are placed at a certain distance. If the force of interaction between two charges is maximum then $\frac{Q}{q_1}=$

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

When a number of charged liquid drops coalesce, which of the following quantity does not change?

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Mention one difference between mass and charge.

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Two small metal balls of different masses $m_1$ and $m_2$ are connected by strings of equal length to a fixed point. When the balls are given equal charges, the angles that the two strings make with the vertical are $30°$ and $60°$, respectively. The ratio $\frac{m_1}{m_2}$ is close to, 

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Name two basic properties of electric charge.

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Suppose the charge of a proton and an electron differ slightly. One of them is $e$, the other is $\left(e+\mathrm{\Delta }e\right)$. If the net electrostatic force and gravitational force between two hydrogen atoms placed at a distance $d$ (much greater than atomic size) apart is zero, then $\mathrm{\Delta }e$ is of the order of [Given mass of hydrogen $m_h= 1.67\times {10}^{–27} \mathrm{kg}$]

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

The dimensions of ${\epsilon }_0$ (permittivity in free space) is

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Two point charges A and B, having charges $+Q$ and $-Q$ respectively, are placed at certain distance apart and force acting between them is $F$. If  $25\mathrm{\%}$ charge of $A$ is transferred to $B$, then the force between the charges becomes

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are $1.6 \mathrm{\AA }$ apart is,
$\left(m_{\mathrm{e}}\simeq 9\times {10}^{-31} \mathrm{kg}, e=1.6\times {10}^{-19} \mathrm{C}\right)$ (Take $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-2}$)

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $800 \mathrm{kg} {\mathrm{m}}^{-3}$ and dielectric constant $21$. If the angle between the strings remains the same after the immersion, then

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

Which experiment established that the electric charge is quantised?

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

If a body gives out ${10}^9$ electrons every second, how much time is required to get a total charge of $1 \mathrm{C}$ from it ?

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Basic Properties of Electric Charge

The number of electrons in one $\mathrm{coulomb}$ charge is