Physics

Electrostatics

303 Questions

Electrostatics deals with electric charges, fields, and potentials at rest. It is a crucial topic for physics sections in engineering and civil services competitive examinations. Review these questions to build a strong understanding of Coulomb law, electric dipoles, Gauss law, and electric flux.

Electric field and potentialElectric dipole momentGauss Law applicationsCoulomb force calculationsCharge distribution on spheresEquipotential surfaces

Electrostatics Questions

Multiple choice physics static electricity properties of charges charge properties of charge

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
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

Multiple choice physics static electricity properties of charges charge properties of charge

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. $\dfrac{q}{6L^2\varepsilon _0}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $\dfrac{q}{\varepsilon _0}$.

Multiple choice physics static electricity properties of charges charge properties of charge

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. $8.854\,C$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice physics static electricity properties of charges charge properties of charge

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

Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice physics static electricity properties of charges charge properties of charge

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. $2000 \mathrm { eV }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

Multiple choice physics static electricity properties of charges charge properties of charge

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. $-5.2 \mu C$
Reveal answer Fill a bubble to check yourself
D Correct answer
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)

Multiple choice physics static electricity properties of charges charge properties of charge

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. $20.8 \times 10^{-18}C$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $1.6\times 10^{-19}\:C$. 

Multiple choice physics static electricity properties of charges charge properties of charge

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
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

Multiple choice physics static electricity properties of charges charge properties of charge

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. ${ E } _{ A }^{ on\quad surface }<{ E } _{ B }^{ on\quad surface }$
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
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
Multiple choice physics static electricity properties of charges charge properties of charge

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 $e$
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
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)

Multiple choice force and torque on a current carrying rectangular loop in a uniform magnetic field torque on current carrying loop force on current carrying conductor magnetic effects of current and magnetism physics

A dipole of dipole moment p is kept at the centre of a ring of radius R and charge Q. The dipole moment has direction along the axis of the ring. The resultant force on the ring due to the dipole is

  1. zero
  2. $\frac{k P Q}{R^3}$
  3. $\frac{2k P Q}{R^3}$
  4. $\frac{k P Q}{R^3}$ only if the charge is uniformly distributed on the ring
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A dipole at the center of a ring produces a field that is symmetric. The force on a charge element dq of the ring is dF = dq * E_dipole. Due to the symmetry of the dipole field and the ring, the net force integrates to zero.

Multiple choice

What is the Debye length?

  1. The distance from a charged surface at which the electrostatic potential is reduced to 1/e of its value at the surface

  2. The distance from a charged surface at which the electrostatic potential is reduced to 1/2 of its value at the surface

  3. The distance from a charged surface at which the electrostatic potential is reduced to 1/4 of its value at the surface

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Debye length is the distance from a charged surface at which the electrostatic potential is reduced to 1/e of its value at the surface.