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Properties of charge - class-XII

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A gold coin has a charge of $+10^{-4} C$. The number of electrons removed from it is:

  1. $10^6$

  2. $625 \times 10^{12}$

  3. $1.6 \times 10^{-25}$

  4. $1.6 \times 10^{13}$


Correct Option: B
Explanation:

The total charge of electrons removed from the coin would be equal to the positive charge acquired by the coin.

Thus, $10^{-4}C=n\times 1.6\times 10^{-19}C$
$\implies n=625\times 10^{12}$

Q(charge)= ?

  1. $\displaystyle n/e$

  2. $\displaystyle ne$

  3. $\displaystyle e/n$

  4. All


Correct Option: B
Explanation:

Q=ne, according to Quantum nature of charge, in nature charge always occurs as an integer multiple of electronic charge i.e. $\displaystyle Q=\pm ne$

A parallel late condenser consists of two circular plate each of radius $8cm$ separated by a distance of $2mm$. It is charged by an external source, with a constant charging current of $0.15$ A. The displacement.curcent is

  1. $0.10A$

  2. $0.15A$

  3. $0.20A$

  4. $0.30A$


Correct Option: A

Choose best option about cavity for a charged metallic sphere: 

  1. Net field inside the cavity is zero

  2. Net field inside the metal is non-zero constant

  3. Potential inside the metal is constant

  4. Potential outside metal is constant


Correct Option: A
Explanation:

Inside the cavity of charged measure sphere net electric field is non zero constant.

$\therefore $ Option $A$ is correct.

Two charges 2$\mathrm { uC }$ and 1$\mathrm { \mu }C$ are placed at adistance of 10$\mathrm { cm }$ . The position of the third charge from2$\mu \mathrm { C }$ between them so that it does not experience any force

  1. $7cm$

  2. $2cm$

  3. $5.858cm$

  4. $8cm$


Correct Option: C

An infinite number of charges each equal to q coulomb are placed along x-axis at x 1, x = 2, x= 8. so on the potential and electric field at x =0 due to this arrangement is

  1. $\dfrac { q } { 2 \pi \varepsilon _ { 0 } } , \dfrac { 3 q } { 4 \pi \varepsilon _ { 0 } }$

  2. $\dfrac { q } { 2 \pi \varepsilon _ { 0 } } \cdot \frac { q } { 3 \pi \varepsilon _ { 0 } }$

  3. $\dfrac { 2 q } { \pi \varepsilon _ { 0 } } , \dfrac { q } { 3 \pi \varepsilon _ { 0 } }$

  4. $\dfrac { q \varepsilon _ { 0 } } { \pi 2 } , \dfrac { q E _ { 0 } } { 3 \pi }$


Correct Option: B

The energy of thermal neutrons is

  1. $< 1 \mathrm { ev }$

  2. $> 1 \mathrm { ev }$

  3. $= 2 \mathrm { Mev }$

  4. $= 4 \mathrm { Mev }$


Correct Option: A

The sum total of the number of electrons in a system may change. The statement is :

  1. true

  2. false

  3. ambiguous

  4. data insufficient


Correct Option: A
Explanation:

The statement is true as electrons can be transferred from one body to the other,  thereby changing the number in the system.  

Quantisation of charge implies :

  1. charge cannot be destroyed

  2. charge exists on particles

  3. there is a minimum permissible charge on a particle

  4. charge, which is a fraction of a charge on an electron is not possible


Correct Option: D
Explanation:

Quantisation of Charge means that we say something has some charge , we mean by that that how many times the charge of electrons it has.  Because  whole charge is associated with an electron.

What is the amount of charge on an electron?

  1. 1.6 $\times 10^{19}$ coulomb

  2. 1.6 $\times 10^{-10}$ coulomb

  3. 1.6 $\times 10^{10}$ coulomb

  4. 1.6 $\times 10^{-19}$ coulomb


Correct Option: D
Explanation:

The charge of an electron is, $e=1.6\times { 10 }^{ -19 }C$.

What is the minimum possible amount of charge?

  1. Electronic charge $e$

  2. Electronic charge $2e$

  3. Electronic charge $\dfrac{e}{2}$

  4. Electronic charge $\dfrac{e}{\sqrt{2}}$


Correct Option: A
Explanation:

The minimum possible charge is equal to the charge of the electron.That is, $e=1.6\times { 10 }^{ -19 }C$.
The electron is a subatomic particle, symbol e, with a negative elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure.

The charge on a body is +1 C. Find the number of electrons in excess or deficit on the body.

  1. 6.25 $\times 10^{1}$ coulomb

  2. 6.25 $\times 10^{-18}$ coulomb

  3. 6.25 $\times 10^{-1}$ coulomb

  4. 6.25 $\times 10^{18}$ coulomb


Correct Option: D
Explanation:

The SI unit of electric charge is Coulomb, One coulomb is equal to about $6.242\times { 10 }^{ 18 }e$. 
One coulomb is defined as the quantity of charge which will pass through the cross section of an electrical conductor while one ampere current is flowing through the conductor in one second. Electric charge is denoted by Q.

The charge on an electron is:

  1. 1 C

  2. +1.6 $\times 10^{-19}$C

  3. -1.6 $\times 10^{-19}$ C

  4. 6.25 $\times 10^{18}$C


Correct Option: C
Explanation:

Answer is C.

Electron charge, fundamental physical constant expressing the naturally occurring unit of electric charge, equal to 1.6021765 1019 coulomb. In addition to the electron, all freely existing charged subatomic particles thus far discovered have an electric charge equal to this value or some whole-number multiple of it.
Hence, the charge of the electron is $-1.6\times { 10 }^{ -19 }C$. The negative sign is due to the negative charge of electrons.

A steady curent ‘i’ is flowing through a conductor of uniform cross-section. Any segment of the conductor has

  1. zero charge

  2. only positive charge

  3. only negative charge

  4. charge proportional to current


Correct Option: A
Explanation:

Any segment of conductor is electrically neutral.
There are fixed positive ions already present that will neutralize the negative charge of the electrons.
No segment serves as the source/sink of charge

Electric charge is due to the loss or gain of .............

  1. protons

  2. neutrons

  3. electrons

  4. none of these


Correct Option: C
Explanation:

Electric charge is due to the loss or gain of electrons.
An atom or group of atoms that have a positive or negative electric charge due to a gain (negative charge) or loss (positive charge) of one or more electrons. Atoms with a positive charge are known as cations; those with a negative charge are anions.

$\displaystyle \frac {4}{25}$ Coulomb of charge contains .................. electrons: 

  1. $10^{15}$

  2. $10^{18}$

  3. $10^{20}$

  4. None of these


Correct Option: B
Explanation:

Answer is C.

The formula for quantisation of charge is given as q=ne.
where, q is the amount of charge in Coulumbs, n is the number of charges and e is the charge on the electron.
In this case, q=4/25 C
So, e = $1.6\times { 10 }^{ -19 }C$.
n can be calculated as n=q/e = $\frac { 4 }{ 25 } \times [\frac { 1 }{ 1.6\times { 10 }^{ -19 }C } ]\quad =\quad { 10 }^{ 18 }$ which is the number of electrons.
Hence, 4/25 
Coulomb of charge contains ${ 10 }^{ 18 }$ electrons:.

Two metallic spheres, one hollow and the other solid, have same diameter. The hollow sphere will hold charge

  1. Same as the solid sphere

  2. 2 times as the solid sphere

  3. $\displaystyle\frac{1}{2}$ times as the solid sphere

  4. Zero


Correct Option: A
Explanation:

The capacity of the metallic sphere is proportional to the radius. It does not matter whether it is solid or hollow. Therefore the hollow sphere will hold same charge as the solid sphere.

Quantisation of charge implies

  1. charge does not exiet

  2. charge exists on particles

  3. there is a minimum permissible magnitude of charge

  4. charge can't be created


Correct Option: C
Explanation:

The word quantised means any quantity is an integral multiple of a minimum value and cannot have any value equal to decimal multiples.

The minimum charge that exists in nature is $1.6\times10^{-19}$ coulombs.
It is the positive value for one proton and negative for an electron.
Any charged body has a positive charge if electrons are less than needed and vice-versa.
Whatever may be the case, the magnitude of charge is always an integral multiple of $1.6\times10^{-19}$ coulombs.
Thus charge is quantised.

Charge on a body can be :

  1. $\displaystyle -1.3e$

  2. $\displaystyle 0.9e$

  3. $\displaystyle \pm 3e$

  4. $\displaystyle 1.5e$


Correct Option: C
Explanation:

Charge on a body is always $\displaystyle \pm e$, $\displaystyle \pm 2e$, $\displaystyle \pm 3e$. It can't be in fraction of e i.e 1.5e, 0.9e or -1.2e. The electronic charge is the minimum possible charge.

Charge on an electron is :

  1. $\displaystyle +e$

  2. $\displaystyle -e$

  3. $\displaystyle \pm e$

  4. All


Correct Option: B
Explanation:

Charge on an electron is -e. SInce, an atom can lose or gain an integer number of electron, so charge on an will be an integer multiple of e.

Charge on a body can be: 

  1. $\displaystyle \pm e$

  2. $\displaystyle \pm 2e$

  3. $\displaystyle \pm 3e$

  4. All


Correct Option: D
Explanation:

Charge on a body is always $\displaystyle \pm e$, $\displaystyle \pm 2e$, $\displaystyle \pm 3e$. It can never be in fraction of e. i.e. 1.5e or -1.2e.

A point charge $+q$ is placed at the centre of a cube of side L. The electric flux emerging from the cube is

  1. $\dfrac{q}{\varepsilon _0}$

  2. Zero

  3. $\dfrac{6qL^2}{\varepsilon _0}$

  4. $\dfrac{q}{6L^2\varepsilon _0}$


Correct Option: A
Explanation:

Since the charge is placed at the centre of the cube, so the electric flux lines move out equally from all sides of the cube. Thus the electric flux emerging from the cube is equal to $\dfrac{q}{\varepsilon _0}$.

Which is the elementary quantum of energy?

  1. Photon

  2. Electron

  3. Proton

  4. Neutron


Correct Option: A
Explanation:

Photon is the elementary quantum of energy.


Option A is correct.

Bulbs in street lightning are all connected in

  1. parallel

  2. series

  3. series-parallel

  4. end-to-end


Correct Option: A
Explanation:

Bulbs in street lightning are all connected in parallel.


Option A is correct.


For testing appliances, the wattage of test lamp should be

  1. very low

  2. low

  3. high

  4. any value


Correct Option: C
Explanation:

For testing appliances, the wattage of test lamp should be high, as higher watt lamps have lower resistance and will not blow up the testing appliacnces.

The additive nature of charge can be explained by the 

  1. Law of Conservation of Electric Charge

  2. Law of Quantisation of Electric Charge

  3. Law of Superposition of Electric Charge

  4. None of these


Correct Option: C
Explanation:

The additive nature of charge is one of the property of electric charge. The entire electric charge of a system is equal to the algebraic sum of electric charges located in the system. This is the law of superimposition of electric charge.

Fill in the blank.

$1$ Coulomb of charge contains_______number of electrons.

  1. $6.25\times 10^{18}$

  2. $3.125\times 10^{18}$

  3. $6.25\times 10^{12}$

  4. $3.125\times 10^{12}$


Correct Option: A
Explanation:

As charge is quantized. 

Total charge, $Q = ne$
$1$ coulomb $=ne \implies$ $n$ $= \dfrac{1} {1\cdot6\times10^{-19}}$

 
 $n$ $=6\cdot25\times10^{18}$

A body has a total charge of $6.4\times  10^{-19}$coulomb. It is :

  1. possible

  2. not possible

  3. may or may not be possible

  4. Data insufficient


Correct Option: A
Explanation:

Total charge must be quantized i.e., it must be a multiple of charge of $e^-$ $=$ $1\cdot 6\times 10^{-19}C$
as $4\times (1\cdot 6\times 10^{-19})=6\cdot 4\times 10^{-19}$
this charge is possible ($4e^-$)

A body has a charge of $9.6 \times 10^{-20}$coulomb. It is :

  1. possible

  2. not possible

  3. may (or) may not possible

  4. Data not sufficient


Correct Option: B
Explanation:

We know that charge must be integral multiples of $1\cdot 6\times 10^{-19}C$ as charge of
one electron $=1\cdot 6\times 10^{-19}C$
We cannot get any charge less than $1\cdot 6\times 10^{-19}$  $\therefore$ we cannot get $9\cdot 6\times 10^{-20}C$

The charges from one body can be Transferred to another body but the total charge of a system ...........

  1. remains Constant

  2. can change

  3. Will increase

  4. will decrease


Correct Option: A
Explanation:

The charges from one body can be transferred to another body but the total charge of a system remains constant.

The electronic charge 'e' is the ............ possible charge.

  1. maximum

  2. minimum

  3. avarage

  4. total


Correct Option: B
Explanation:

Charge is an integral multiple of e, minimum charge possible is equal to e which is $1.6 \times 10^{-19}$ C.Hence correct answer is option B.

If the number of electric lines of force emerging out of a closed surface is 1000, then the charge enclosed by the surface is

  1. $8.854 \times {10^{ - 9}}C$

  2. $8.854 \times {10^{ - 4}}C$

  3. $8.854 \times {10^{ - 1}}C$

  4. $8.854\,C$


Correct Option: A
Explanation:

Given that $\phi $, no. of field lines $=1000$

From gauss law,
$\phi =\dfrac { { Q } _{ inc } }{ { \varepsilon  } _{ 0 } } $
$\therefore \quad 1000=\dfrac { { Q } _{ inc } }{ 8.85\times { 10 }^{ -12 } } $
$\Rightarrow \quad { Q } _{ inc }=8.85\times { 10 }^{ -12 }\times 1000$
                   $=8.854\times { 10 }^{ -9 }C$

$\therefore $  Option (A) is the correct answer.

Two insulated charged spheres of radii $20cm$ and $25cm$ respectively and having equal charge $q$ are connected by a copper wire and then they are separated

  1. Both the spheres will have same charge $q$

  2. The charge on $20cm$ sphere will be greater than on the $25cm$ sphere

  3. The charge on $25cm$ sphere will be greater than on the $20cm$ sphere

  4. Both have same charge density 


Correct Option: B
Explanation:

After redistribution, charges on them will be different, but they will acquire common potential i.e.

$k\frac{Q _1}{r _1}=k\frac{Q _2}{r _2}\Rightarrow\frac{Q _1}{Q _2}=\frac{r _1}{r _2}$
As,
$\sigma=\frac{Q}{4\pi r^2}$
$\frac{\sigma _1}{\sigma _2}=\frac{Q _1}{Q _2}\times \frac{r _2^2}{r _1^2}\Rightarrow \frac{\sigma _1}{\sigma _2}=\frac{r _2}{r _1}$
$\sigma \propto \frac{1}{r}$ i.e. surface charge density on smaller sphere will be more.

There are $4\times { 10 }^{ 23 }$ atoms in a metal sphere. If one electron is removed from $0.1\%$ of atoms, what will be the charge on the sphere?

  1. $-6.4C$

  2. $64C$

  3. $0.64C$

  4. $-64C$


Correct Option: D
Explanation:
Given, 

$n=4\times 10^{23}\times 0.1$%

$n=4\times 10^{23}\times \dfrac{0.1}{100}=4\times 10^{20}$

$e=1.6\times 10^{-19}C$

The charge is quantised, $q=ne$

$q=4\times 10^{20}\times 1.6\times 10^{-19}=64C$

The electron is negative charge particle.

So,$q=-64C$

The correct option is D.

The density of field lines surrounding any given object reveal information about the

  1. the nature of charge on the source charge.

  2. the quantity of charge on the source charge.

  3. both A and B

  4. it reveals no information


Correct Option: B
Explanation:

The density of field lines shows the strength of field, and hence reveal the information about the magnitude of charge that is quantity of charge on the source.

The product of potential difference and charge is measured in 

  1. colulomb

  2. volt

  3. juole

  4. watt


Correct Option: A

The energy acquired by a charge of $8 \times 10 ^ { - 19 } { C }$ when passed through a potential difference of $200\ volt$

  1. $500 \mathrm { eV }$

  2. $1000 \mathrm { eV }$

  3. $1500 \mathrm { eV }$

  4. $2000 \mathrm { eV }$


Correct Option: B
Explanation:

$\begin{array}{l} U=qV \ =8\times { 10^{ -19 } }\times 200J \ =\dfrac { { 8\times { { 10 }^{ -19 } }\times 200 } }{ { 1.6\times { { 10 }^{ -19 } } } } eV \ =1000ev \ Hence,\, the\, option\, B\, is\, the\, correct\, answer. \end{array}$

Two charges of equal magnitude and at a distance'r' exert a force $F$ on each other. If the charges are halved and distance between them is doubled, then the new force acting on each charge is

  1. $F / 8$

  2. $F / 4$

  3. $4 F$

  4. $F / 16$


Correct Option: D
Explanation:

Original force$,$

$F = k\dfrac{{q\,q}}{{{r^2}}}$
New force$,$
$F = k\dfrac{{\dfrac{q}{2}\,\dfrac{q}{2}}}{{{{\left( {2r} \right)}^2}}} = \dfrac{1}{{16}}F = \dfrac{F}{{16}}$
Hence,
option $(D)$ is correct answer. 

Mark the correct options : 

  1. The total charge of the universe is constant.

  2. The total positive charge of the universe is constant.

  3. The total negative charge of the universe is constant.

  4. The total number of charged particles in the universe is constant.


Correct Option: A
Explanation:

The law of conservation of charges states that electric charge can neither be created nor destroyed.
Hence the net quantity of electric charge of the universe is always conserved. 

$\displaystyle \frac {4}{25}$ Coulomb of charge contains .......... electrons

  1. $10^{15}$

  2. $10^{18}$

  3. $10^{20}$

  4. None of these


Correct Option: B
Explanation:

The formula for quantization of charge is given as q=ne.
where q is the amount of charge in Columbu's, n is the number of charges and e is the charge on the electron.
In this case, q=4/25 C
So, e = $1.6\times { 10 }^{ -19 }C$.
n can be calculated as n=q/e = $\frac { 4 }{ 25 } \times [\dfrac { 1 }{ 1.6\times { 10 }^{ -19 }C } ]\quad =\quad { 10 }^{ 18 }$ which is the number of electrons.
Hence, 4/25 Coulomb of charge contains ${ 10 }^{ 18 }$ electrons.

The conservation of electric charge implies that

  1. charge cannot be created

  2. charge cannot be destroyed

  3. the number of charged particles in the universe is constant

  4. simultaneous creation of equal and opposite charges is permissible


Correct Option: A,B,C
Explanation:

A, B and C are correct. 

A substance is neutral due to the presence of equal magnitude of positive and negative charge on it.
Although D is possible in radioactivity and its reactions, it is not related to the statement of the question

The number of electrons for one coulomb of charge are:

  1. $\displaystyle 6.25\times { 10 }^{ 23 }$

  2. $\displaystyle 6.25\times { 10 }^{ 21 }$

  3. $\displaystyle 6.25\times { 10 }^{ 18 }$

  4. $\displaystyle 6.25\times { 10 }^{ 19 }$


Correct Option: C
Explanation:

1 electron carries a charge of $1.6 \times 10^{-19}$ coulomb 

So, No.of electron in one coulomb
$\dfrac{1}{1.6 \times 10^{-19}} = \dfrac{10^{19}}{1.6} = 6.25 \times 10^{18}$

How many electrons make up a charge of $\displaystyle 20\mu C$ ?

  1. $\displaystyle 1.25\times { 10 }^{ 14 }$

  2. $\displaystyle 2.23\times { 10 }^{ 14 }$

  3. $\displaystyle 3.25\times { 10 }^{ 14 }$

  4. $\displaystyle 5.25\times { 10 }^{ 14 }$


Correct Option: A
Explanation:

Charge on an electron $= 1.6 \times 10^{-19}$coulomb

no of electrons required $ = \dfrac{20 \times 10^{-6}}{1.6 \times 10^{-19}} = 1.25 \times 10^{14}$

When resistance element of a heater fuses and then we reconnect it after removing a portion of it, the power of the heater will :

  1. decrease

  2. increase

  3. remain constant

  4. none


Correct Option: B
Explanation:

When ressitance element of a heater fuses and then we reconnect it after removing a portion of it, the power of the heater will increases because the resistance of wire decreases due to decrease in length of it. 


Option B is correct.

Sparking occurs when a load is switched off because the circuit has high :

  1. resistance

  2. inductance

  3. capacitance

  4. impedance


Correct Option: B
Explanation:

When circuit has high inductance then sparking occurs.


Option B is correct.


When electric current passes through a bucket full of water , lot of bubbling is observed. This suggests that the type of supply is

  1. AC

  2. DC

  3. any of the above two

  4. None of the above


Correct Option: B
Explanation:

When a dc current is passed through water, the electrolysis of water molecules $(H _{2}O)$ takes place i.e, water gets split into hydrogen and oxygen gases. The bubbles are these gases escaping.

How many electronic charges from $1$ coulomb?

  1. $9.1\times 10^{-31}$

  2. $1.6\times 10^{18}$

  3. $62.5\times 10^{17}$

  4. $1.76\times 10^{11}$


Correct Option: C
Explanation:

Let the total electronic charge be n

$1=ne=n\times 1.6\times 10^{-19}$
$n=62.5\times 10^{17}$

The net charge inside an isolated system is

  1. conserved

  2. variable

  3. zero

  4. infinite.


Correct Option: A
Explanation:

According to law of conservation of charge, the net charge inside an isolated system is conserved. 

A charge of $-1C$ contains $n$ electrons, then $n=?$

  1. $6.25 \times 10^{-20}$

  2. $6.25 \times 10^{19}$

  3. $6.25 \times 10^{18}$

  4. $6.25 \times 10^{-19}$


Correct Option: C
Explanation:

Here, $n(-e)=Q=-1C$ or $n=1/e=\dfrac{1}{(1.6\times 10^{-19})}=6.25\times 10^{18}$

If $Q _1 = 5\mu C$, $Q _2 = 3 \mu C$ and $Q _3= -2 \mu C$, then the net charge in the system is :

  1. $-6 \mu C$

  2. $6 \mu C$

  3. $8 \mu C$

  4. $-2 \mu C$


Correct Option: B
Explanation:

The net charge of the given system is $Q=Q _1+Q _2+Q _3=(5+3-2)\mu C=6\mu C$

Charge separation can be affected by

  1. contact

  2. pressure

  3. heat

  4. charge


Correct Option: A,D
Explanation:
Charge separation can be affected by -
(a) Contact
(b) Charge
Because contact of force will be affected for the charge separation and charge accumulation will be the affected of charge separation pressure and heat also.

During charge separation, there is a

  1. creation of charge

  2. creation of energy

  3. creation of charged particles

  4. creation of neutrons


Correct Option: C
Explanation:

Charge separation is the process of exciting an electron in an atom to a higher energy level and then making it leave the atom to a hereby electron acceptor thus creating charged particle.

A metal sphere has a charge of $- 6 \mu C$. When $5 \times 10^{12} $ electrons are removed from the sphere, what would be net charge on it?

  1. $-6.8 \mu C$

  2. $6.8 \mu C$

  3. $5.2 \mu C$

  4. $-5.2 \mu C$


Correct Option: D
Explanation:

Charge removed=$-e\times n=-1.6\times 10^{-19}\times 5\times 10^{12}=-8\times 10^{-7}=-0.8\mu C$


Hence, charge on sphere=$-6-(-0.8)=-5.2\mu C$

Answer-(D)

Only the integral number of electrons which is transferred from one body to another, i.e. $\pm ne$. This is represented as

  1. Superposition of charge

  2. Quantisation of charge

  3. Conservation of charge

  4. Addition of charge


Correct Option: B
Explanation:

The transfer of electrons from one body to other leads to charging of bodies. It is found that charge on any body is always equal to integral multiple of charge on electron. This property of charge is known as Quantisation of electric charge according to which, $Q=ne$
$Q=$ total charge transferred
$n=$ number of electrons transferred
$e=$ charge on one electron
$n=1, \pm 2.....$ and so on.

A copper slab of mass $2 g$ contains $2 \times 10^{22}$ atoms. The charge on the nucleus of each atom is $29 e$. What fraction of the electrons must be removed from the sphere to give it a charge of $+2\mu C$? 

  1. $58 \times 10^{22}$

  2. $1.25 \times 10^{13}$

  3. $2.16 \times 10^{11}$

  4. $2.16 \times 10^{-11}$


Correct Option: D
Explanation:
Given a mass of copper slab $=2\, g$ contains $2\times 10^{22}$ atoms.
Charge on nucleus of each atom $=29e$
We have to find the fraction of electrons that must be removed from sphere to give it $+2\mu C$ charge.
We solve it as follows:
Total number of electrons in sphere $=29\times 2\times 10^{22}$
Number of electrons $=\dfrac qe$
$=\dfrac{2\times 10^{-6}}{1.6\times 10^{-19}}$
$=1.25\times 10^{13}$
Fraction of electrons removed $=\dfrac{1.25\times 10^{13}}{Total\; number \; of \;electrons \; in\; sphere}$
$=\dfrac{1.25\times 10^{13}}{29\times 2\times 10^{22}}$
$=2.16\times 10^{-11}$

Which of the following charges is/are impossible?

  1. $4.8 \times 10^{-18}C$

  2. $5.8 \times 10^{-18}C$

  3. $12.8 \times 10^{-18}C$

  4. $20.8 \times 10^{-18}C$


Correct Option: B
Explanation:
From $Q=ne$,
where $Q =$ total charge
$n=$ number of electrons
$e=$ charge on one electron 
So, only that charge is possible for which charge is whole multiple of $1.6\times 10^{-19}$ (i.e, charge on one electron).
We can see that multiplying $1.6\times 10^{-19}$ with $30$ gives $A$
Multiplying $1.6\times 10^{-19}$ with $80$ gives $C$
 Multiplying $1.6\times 10^{-19}$ with $130$ gives $D$
We can see that a, c and d are multiple of charge $1.6\times 10^{-19}\:C$.
Only $5.8\times 10^{-18}\: C$ given in B) option is not a multiple of $1.6\times 10^{-19}\:C$. 

Charge can be a multiple of $e$, i.e. $ne$. Which of the following can be a value of $n$?

  1. 27

  2. 1.5

  3. 30.5

  4. 0.99999


Correct Option: A
Explanation:

Charge has to be an integral multiple of electronic charge e.

If a conductor has $10^8$ number of electrons , then the total charge of the conductor is:

  1. $+1.6 \times 10^{-19}$ C

  2. $-1.6 \times 10^{-19}$ C

  3. $+1.6 \times 10^{-11}$ C

  4. $-1.6 \times 10^{-11}$ C


Correct Option: D
Explanation:

Any charge exists in discrete lumps or packets of a certain minimum charge e where e is the charge of an electron. According to quantization of charge, the charge on a body can be only an integral multiple of charge on the electron i.e., $q = ne$ where n = 1, 2, 3 and $e=1.6\times { 10 }^{ -19 }$ C.

So, for the given case, $q=10^8 \times (-1.6 \times 10^{-19})$ C$=-1.6 \times 10^{-11}$ C.

When a glass rod is rubbed against silk.

  1. Glass rod loses electrons and becomes positively charged

  2. Silk loses electrons and becomes positively charged

  3. Glass rod losses electrons and becomes negatively charged

  4. Silk loses electrons and becomes negatively charged


Correct Option: A
Explanation:

 Due to rubbing, heat is generated which supplies energy for removal of electrons. As the work function of the glass rod is smaller than the silk cloth, it easily loses electrons to the silk cloth.

How many electronic charges form 1 coulomb?

  1. $9.1\times 10^{-31}$

  2. $1.6\times 10^{18}$

  3. $62.5\times 10^{17}$

  4. $1.76\times 10^{11}$


Correct Option: C
Explanation:

$q=ne$
$\therefore n=\dfrac {q}{e}$
Given $q=1C$
$e=-1.6\times 10^{-19}C$
$n=\dfrac {1C}{1.6\times 10^{-19}}$
$6.25\times 10^{18}$ or $62.5\times 10^{17}$

A spherical metal shell $A$ of radius ${R} _{A}$ and a solid metal sphere $B$ of radius ${R} _{8}\left( <{ R } _{ A } \right)$ are kept far apart and each is given charge $+Q$. Now they are connected by a thin metal wire. Then 

  1. ${ E } _{ A }^{ inside }=0$

  2. $\quad { Q } _{ A }>{ Q } _{ B }$

  3. $\dfrac { { \sigma } _{ A } }{ { \sigma } _{ B } } =\dfrac { { R } _{ B } }{ R _{ A } }$

  4. ${ E } _{ A }^{ on\quad surface }<{ E } _{ B }^{ on\quad surface }$


Correct Option: A,B,C,D
Explanation:
Electric field inside a spherical metallic shell with charge on surface $=0$
$\therefore (a)$ is correct
On connecting Both with wise
Electric potential will be equal say $V$
$\therefore \dfrac{1}{4\pi Co}\dfrac{Q _A}{R _A}=\dfrac{1}{4\pi Co}\dfrac{Q _B}{R _B}=V$
as $R _A> R _B\therefore Q _A > Q _B$ Hence $(b)$ is correct
as $\dfrac{\sigma _A}{\sigma _B}=\dfrac{Q _B}{4\pi R _{B}^{2}}=\dfrac{R^{2}B}{R^{2}A}\times \dfrac{4\pi Co R _{A}V}{4\pi Co R _{A}R}$
$\dfrac{\sigma A}{\sigma B}=\dfrac{R _B}{R _A}$             $(C)$ is correct
Also $E _{A}=\dfrac{\sigma _A}{\sigma _B}=\dfrac{R _B}{R _A}<1\therefore E _A < E _B$
Hence $(d)$ is correct

Electron accelerated by potential $V$ are diffracted from a crystal. If $d=1 A$ and $i = 30^\circ $. $V$ should be about  $h = 6.6 \times {10^{ - 24}}Js\,{m _e} = 9.1 \times {10^{ - 33}}kg.e = 1.6 \times {10^{ - 19}}C$

  1. $2000 V$

  2. $50 V$

  3. $500 V$

  4. $1000 V$


Correct Option: B
Explanation:

$d=1A$

$i={ 30 }^{ o  }$
$\theta ={ 60 }^{ o  }$
$h=6.6\times { 10 }^{ -34 }Js$
${ m } _{ e }=9.1\times { 10 }^{ -31 }kg$
$e=1.6\times { 10 }^{ -19 }c$
$n\lambda =2dsin\theta $
$\lambda =\dfrac { 2\times 1A\times sin{ 60 }^{ o  } }{ 1 } $
$\lambda =\sqrt { 3A } $
$\sqrt { V } =\dfrac { 1.27\times { 10 }^{ -10 } }{ \sqrt { 3 } \times { 10 }^{ -10 } } =50.18volts$

All free electric charges can be 
($e=$ single unit of charge i.e. the magnitude of charge on electron )

  1. odd multiples of $e$

  2. fractional multiples of $e$

  3. even multiples of $e$

  4. negative multiples of $e$


Correct Option: A,C,D
Explanation:

Charges are acquired by either gain or loss of electrons .

And electron transfer can occur only in form of integers, fraction of electron can't be shared.

Hence, charge on a body can be positive or negative integral multiple of $e$.

Answer-(A),(C),(D)

Charge $q$ on a body in terms of transfer of electrons can be expressed as
( $n=$ net number of electrons transacted)

  1. $ q = ne$

  2. $ q = \dfrac{e}{n}$

  3. $ q = - \dfrac{e}{n}$

  4. None of these


Correct Option: A
Explanation:

Charge on each electron$=e$


If  n be the number of electrons transferred, then charge $q=ne$.

Answer-(B)

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