Physics

Electrostatics

299 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 potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

A uniform electric field of magnitude $290 V/m$ is directed in the positive $x$ direction. A $+13.0 \mu C$ charge moves from the origin to the point $(x, y) = (20.0 cm, 50.0 cm).$

What is the change in the potential energy of the charge field system?

  1. $-754J$
  2. $-754mJ$
  3. $-754kJ$
  4. $-754\mu J$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given electric field, $\overrightarrow{E}=290\, V/m$ directed along $+x$ direction.
Charge $=+13\mu C$ moves from origin to point $(x,y)=(20\, cm , 50\, cm)$.
We have to find the charge in potential energy of the charge field system.
We know, the change in potential energy  $=$ charge $\times $ change in potential
i.e, $\Delta U=q\Delta V$
But, $\Delta V=-Ed$
$\Delta U=-qEd$
$=-13\times 10^{-6}\times 290\times 20\times 10^{-2}$
$=0.000754\, J$
$=-754\times 10^{-6}\, J$
Here $d=20\, cm$, since electric field is along positive $x-$axis.
Multiple choice mutual inductance electromagnetic induction electromagnetic induction and alternating currents physics

The electric field of an electromagnetic wave is given by, $E=(50N^{-1})\, \sin { \omega  } (t-x/c)$. Find the energy contained in a cylinder of cross section $10cm^2$ and length $50 cm$ along the x-axis.

  1. $5.5\times 10^{-12}J$
  2. $4.5\times 10^{-12}J$
  3. $5\times 10^{-13}J$
  4. $3.5\times 10^{-10}J$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The energy density of an EM wave is u = (1/2) * epsilon0 * E^2 + (1/2) * (B^2 / mu0). For an EM wave, the average energy density is u_avg = (1/2) * epsilon0 * E0^2. The total energy is U = u_avg * Volume. Volume = Area * length = 10 * 10^-4 m^2 * 0.5 m = 5 * 10^-4 m^3. E0 = 50 V/m. u_avg = 0.5 * 8.85 * 10^-12 * 50^2 = 1.1 * 10^-8 J/m^3. U = 1.1 * 10^-8 * 5 * 10^-4 = 5.5 * 10^-12 J.

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

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

$\therefore $ Option $A$ is correct.

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

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. $8cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a charge to experience no force, the electric fields from the two charges must be equal and opposite. Setting k(2)/x^2 = k(1)/(10-x)^2 leads to 2(10-x)^2 = x^2, which simplifies to sqrt(2)(10-x) = x. Solving for x gives x = 10*sqrt(2)/(1+sqrt(2)) approximately 5.858 cm.

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

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. $\dfrac { q \varepsilon _ { 0 } } { \pi 2 } , \dfrac { q E _ { 0 } } { 3 \pi }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics static electricity properties of charges charge properties of charge

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 $\dfrac{e}{\sqrt{2}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

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)