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 electrostatics field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

Two charges $+Q$ and $-2Q$ are located at points $A$ and $B$ on a horizontal line as shown in the diagram.
The electrical field is zero at a point which is located at finite distance :

  1. On the perpendicular bisector of $AB$
  2. Left of $A$ on the line
  3. Between $A$ and $B$ on the line
  4. Right of $B$ on the line
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ E _1 $ = Electrical field due to $+Q$
$E _2$ = Electrical feild due to $-2Q$
There resultant is $0$ at this point 

Multiple choice chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

A solid ball of radius R has a charge density p given by $p=p _0(1 -r/R)$ for $ 0 \leq r \leq R.$ The electric field outside the ball is:

  1. $\dfrac{p _0R^3}{\epsilon _0r^2}$
  2. $\dfrac{p _0R^3}{12\epsilon _0r^2}$
  3. $\dfrac{4p _0R^3}{3\epsilon _0r^2}$
  4. $\dfrac{3p _0R^3}{4\epsilon _0r^2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$According\, to\, question..................... \ q=\int  _{ 0 }^{ R }{ pdv }=\int  _{ 0 }^{ R }{ po }\left( { 1-\dfrac { r }{ R }  } \right) \, .\, 4\pi { r^{ 2 } }drr \ \Rightarrow q=po.4\pi \, \left[ { \int  _{ 0 }^{ R }{ { r^{ 2 } }dr-\int  _{ 0 }^{ R }{ \dfrac { { { r^{ 3 } } } }{ R } dr } } } \right]  \ \Rightarrow q=po.4\pi \left( { \dfrac { { { R^{ 3 } } } }{ 3 } -\dfrac { { { R^{ 3 } } } }{ 4 }  } \right) =po\left( { 4\pi  } \right) \dfrac { { { R^{ 3 } } } }{ { 12 } }  \ \, \, \, \, \, \, \therefore \, \, \, q=\dfrac { { po.\pi { R^{ 3 } } } }{ 3 }  \ E=\dfrac { 1 }{ { 4\pi { \in _{ 0 } } } } \times \, \dfrac { q }{ { { r^{ 2 } } } } =\dfrac { 1 }{ { 4\pi { \in _{ 0 } } } } \, \times \dfrac { { po\, .\pi { R^{ 3 } } } }{ { 3{ r^{ 2 } } } } =\dfrac { { po\, .{ R^{ 3 } } } }{ { 12{ \in _{ 0 } }{ r^{ 2 } } } }  \ \, \, \, \therefore \, \, \, \, E=\dfrac { { po\, .{ R^{ 3 } } } }{ { 12{ \in _{ 0 } }{ r^{ 2 } } } }  \ there\, for\, the\, correct\, option\, is\, B.$

Multiple choice

When two bodies are rubbed against each other, they acquire

  1. equal and like charges

  2. equal and unlike charges

  3. unequal and like charges

  4. unequal and unlike charges
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When two objects are rubbed together, electrons are transferred from one to the other. This leaves one object with a positive charge and the other with an equal negative charge, resulting in equal and unlike charges.

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

Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding . The charges on the two rings are + q and -q . The potential difference between the centres of the two rings is

  1. $\frac {{ Q.R }\quad} {\quad { 4\pi }{ \varepsilon } _{ 0 }{ d }^{ 2 }}$
  2. $\frac { Q }{ 2\pi { \varepsilon } _{ 0 } } [\frac { 1 }{ R } -\frac { 1 }{ \sqrt { { R }^{ 2 }+{ d }^{ 2 } } } ]$
  3. $\frac { Q }{ { 4\pi \varepsilon } _{ 0 } } [\frac { 1 }{ R } -\frac { 1 }{ \sqrt { { { R }^{ 2 } }+{ { d }^{ 2 } } } } ]$

  4. 0
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Two thin wire ring each having a radius $=R$

distance $=d$
two rings are $+q$ and $-q$.
$PD=\dfrac { 1 }{ 4\pi { \epsilon  } _{ 0 } } \dfrac { QR }{ { d }^{ 2 } } $
Now in this question, we get the solution.

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

what is the potential difference between two points, if 2J of work must be done to move a 4 mC charge from one point to another is:

  1. 50 V

  2. 500 V

  3. 5 V

  4. 5000 V
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Answer is B.

The total work done = energy transferred.
so, we might see the equation energy = voltage x charge, E = V * Q, written as, 
work = voltage x charge, W = V * Q.
In this case, the charge is 4 mC, that is, 0.004 C and work done is 2 J.
Therefore, V=W/Q = 2/0.004 = 500 V.
Hence, the potential difference between two points if 2 J of work must be done to move a 4 mC charge from one point to another is 500 V.

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

A point charge q is rotated along a circle in the electric field generated by another point charge Q. The work done by the electric field on the rotating charge in one complete revolution is_______

  1. zero

  2. positive

  3. negative

  4. zero if the charge Q is at the center and nonzero otherwise.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The net displacement round one complete circle is 0.

So, the work done is 0.

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

$100J$ of work is done when $2 \mu C$ charge is moved in an electric field between two points. The p.d. between the points is

  1. $2\times10^{-4}V$
  2. $2\times10^{-8}V$
  3. $2\times10^{-6}V$
  4. $5\times10^{7}V$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know work done $=q\Delta V $
Where $\Delta V $ is change in potential $V _2-V _1$
$100=\Delta V\times 2\times 10^{-6}$
$50\times 10^6=\Delta V$
$\therefore p\cdot d= 5\times 10^7 V$

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

A hollow metal sphere of radius $5\ cm$ is charged such that the potential on its surface is $10$ volts. The potential of the centre of the sphere is:

  1. zero
  2. $10$ volts
  3. Same as at a point $5\ cm$ away from the surface.
  4. Same as at a point $25\ cm$ away from the surface.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
For hollow spherical conductor -
$\Rightarrow$ Potential on its surface $=$ Potential on center $= 10\;volts.$
Because, the electric field inside the spherical shell is zero, due to which the potential inside the shell is constant and will be equal to the potential at the surface.
Hence, the answer is $10\;volts.$
Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

A spherical shell of radius $R _1$ with uniform charge $q$ is expanded to a radius $R _2$. Find the work performed by the electric forces during the shell expansion from $R _1$ to radius $R _2$.

  1. $\dfrac{q^2}{2\pi in _0}\left(\dfrac{1}{R _1} - \dfrac{1}{R _2}\right)$
  2. $\dfrac{q^2}{3\pi in _0}\left(\dfrac{1}{R _1} - \dfrac{1}{R _2}\right)$
  3. $\dfrac{q^2}{5\pi in _0}\left(\dfrac{1}{R _1} - \dfrac{1}{R _2}\right)$
  4. $\dfrac{q^2}{8\pi in _0}\left(\dfrac{1}{R _1} - \dfrac{1}{R _2}\right)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Spherical shell of radius $={ R } _{ 1 }$
charge $=q$
work done $=W=q\left( { V } _{ B }-{ V } _{ A } \right) $
${ V } _{ A }=\dfrac { { K } _{ q } }{ { R } _{ 1 } } $
${ V } _{ B }=\dfrac { { K } _{ q } }{ { R } _{ 2 } } $
$W=q\left( \dfrac { { K } _{ q } }{ { R } _{ 1 } } -\dfrac { { K } _{ q } }{ { R } _{ 2 } }  \right) $
     $=\dfrac { { q }^{ 2 } }{ 8\pi { \epsilon  } _{ 0 }{ n } _{ 0 } } \left( \dfrac { 1 }{ { R } _{ 1 } } -\dfrac { 1 }{ { R } _{ 2 } }  \right) $    (Proved).
Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

Two insulated charged spheres of radii ${R} _{1}$ and ${R} _{2}$ having charges ${Q} _{1}$ and ${Q} _{2}$ respectively are connected to each other, then there is:

  1. no change in the energy of the sytem

  2. an increase in the energy of the system

  3. always a decrease in the energy of the system
  4. a decrease in energy of the system unless ${q} _{1}{R} _{2}={q} _{2}{R} _{1}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Two insulated charged spheres of radii $ R _1,R _2$having charges $q _1,q _2$respectively are brought in contact with each other.

Charges will flow across the point of contact from where they are connected until their potential at their surfaces became same. 
Energy is decreased because system changes to get stability.
Potential at their surfaces are same,
So,
$V _1=V _2$
$\dfrac{Kq _1}{R _1}=\dfrac{Kq _2}{R _2}$
$q _1R _2=q _2R _1$
Hence Proved.

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

A charge $10$ esu is placed at a distance of $2$ cm, from a charge$ 40$ esu and $4$ cm. from another charge -$20$ esu. The potential energy of the charge $10$ esu is :- (In ergs)

  1. $87.5$
  2. $112.5$
  3. $150$
  4. $zero$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The electrostatic potential energy of a system of point charges is the sum of potential energies of all unique pairs. Using U = (q1*q2)/r with charges in esu and distances in cm, calculate the interaction energy between each pair: (10*40)/2 + (10*(-20))/4 + (40*(-20))/dist, which simplifies correctly to 150 ergs.

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

Calculate the electrostatic potential energy of two electrons separated bt 3 $\overset { \circ  }{ A } $ in vacuum

  1. $7.69\times10^{-19} J$
  2. $8.69\times10^{-19} J$
  3. $5.69\times10^{-19} J$
  4. $6.69\times10^{-19} J$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

U = k * q1 * q2 / r. k = 9 * 10^9, q = 1.6 * 10^-19 C, r = 3 * 10^-10 m. U = (9 * 10^9 * (1.6 * 10^-19)^2) / (3 * 10^-10) = 7.68 * 10^-19 J. Option B is the closest value provided.