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 physics magnetic fields and electromagnetism contact and non-contact forces comparing force in magnetic, electric and gravitational fields identifying forces

Four point charge of $+10^{-7}C, -10^{-7}C, -2\times 10^{-7}C$ and $+2\times 10^{-7}C$ are placed respectively at the corners $A, B, C, D$ of a $0.05\ m$ square. Find the magnitude of the resultant force on the charge at $D$.

  1. $0.2\ dyne$
  2. $0.2\ newton$
  3. $2\ dyne$
  4. $0.02\ newton$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole of moment $ \vec { p } $ is placed in a uniform electric field$\vec { E }$ . Then
(i) The torque on the dipole is $\vec { p } \times \vec { E } $.
(ii) The potential energy of the system is $\vec { p } \cdot \vec { E } $.
(iii) The resultant force on the dipole is zero.
Choose the correct option.

  1. (i), (ii) and (iii) are correct

  2. (i) and (iii) are correct and (ii) is wrong

  3. Only (i) is wrong

  4. (i) and (ii) are correct and (iii) is wrong
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a uniform electric field, $\vec { E } $, dipole experiences a torque $\vec { \tau  } $ given by $\vec { \tau  } =\vec { p } \times \vec { E } $ but experiences no force. The potential energy of the dipole in a uniform electric field $\vec { E } $ is $U=-\vec { p } .\vec { E } $

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole of length 20 cm having $\pm3 \times { 10 }^{ -3 }$ C charge placed at 60 with respect to a uniform electric field experiences a torque of magnitude 6 N m. the potential energy of the dipole is:

  1. -2$\sqrt { 3 }$ J
  2. 5$\sqrt { 3 }$ J
  3. -3$\sqrt { 2 }$ J
  4. 3$\sqrt { 5 }$ J
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Here,

Length of dipole $2a= 20\ cm=0.2\ m$
Charge, $q= \pm 3\times 10^{-3}\ C$,             $\theta=60^o$
Torque, $\tau=6\ Nm$
As, $\tau=pEsin\ \theta$
or $E=\dfrac{\tau}{psin \theta}= \dfrac{\tau}{q(2a)sin \theta}(\because p=q(2a)$

$\therefore E=\dfrac{6}{3\times 10^{-3}\times 20 \times 10^{-2} \times sin\ 60^o}= \dfrac{10^5}{5\sqrt 3} NC^{-1}$

Potential energy of dipole, $U=-pEcos \theta=-q(2a) E cos \theta $

$\implies U= -3\times 10^{-3}(20 \times 10^{-2} )\dfrac{10^5}{5\sqrt 3} cos 60^o= -2\sqrt 3\ J$

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole is kept on the axis of a uniformly charged ring at distance $\frac{R}{\sqrt{2}}$ from the centre of the ring. The direction of the dipole moment is along the axis. The dipole moment is P, charge of the ring is Q & radius of the ring is R. The force on the dipole is ___________________.

  1. (a) $\frac{4 k P Q}{3\sqrt{3} R^{2}}$
  2. (b) $\frac{4 k P Q}{3\sqrt{3} R^{3}}$
  3. (c) $\frac{2 k P Q}{3\sqrt{3} R^{2}}$

  4. (d) zero
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The electric field on the axis of a ring is E = kQx / (R^2 + x^2)^(3/2). For a dipole at x = R/sqrt(2), the field gradient exerts a force F = p * (dE/dx). Calculating the derivative and substituting gives the force.

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

Two electric dipoles of dipole moment $2 \space cm$ and $4 \space cm$ respectively are kept inside a cube of side $'a' \space m$. Total electric flux linked with the cube is (in SI units)

  1. $\dfrac{6}{\varepsilon _0}$
  2. $\dfrac{2}{\varepsilon _0}$
  3. $\dfrac{4}{\varepsilon _0}$

  4. none of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since net charge $=0$

$\therefore \phi =0$
$\therefore$ option $D$ is correct answer.

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

A neutral water molecule $ (H _2 O) $ in its vapour state has an electric dipole moment of $ 2 \times 10^{-24} C-m. $ If the molecule is placed in an electric field of $ 2 \times 10^{4} NC^{ _1} $ , the maximum torque that the field can exert on it is nearly.

  1. $ 4 \times 10^{-20} N-m $
  2. $ 6 \times 10^{-20} N-m $
  3. $ 8 \times 10^{-20} N-m $
  4. $ 2 \times 10^{-18} N-m $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P = 2 \times 10^{-24}Cm$


$E = 2 \times 10^{4}NC$

$\tau = EP = 2 \times 10^{-24} \times 2 \times 10^{4} = 4 \times 10^{-20}Nm$

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

A dipole is placed parallel to the electric field. If W is the work done in rotating the dipole by $60$, then the work done in rotating it by $180$ is:

  1. $ 2W$
  2. $ 3W$
  3. $ 4W$
  4. $ W/2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done in rotating dipole by $\theta \,$ angle from eqbm. ,$W = PE\left( {1 - \cos \theta } \right)$

$\begin{array}{l}W = PE\left( {1 - \cos 60^\circ } \right)\ = PE\left( {1 - \frac{1}{2}} \right) = \frac{{PE}}{2}\or\,\,\,PE = 2W\W' = PE\left( {1 - \cos 180^\circ } \right)\ = PE\left( {1 - \left( { - 1} \right)} \right)\ = 2PE = 2 \times 2W = 4W\end{array}$

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

Two charges of charge $-4\mu C$ and $+4\mu C$ are placed of the point $A(1, 0, 4)$ and $B(2, -1, 5)$ located in an electric field $E = 0.20\hat {i} V/ C-m$. Then, torque acting on the dipole will be

  1. $2.31\times 10^{-4} N/m$
  2. $7.98\times 10^{-4} C/m$
  3. $7.11\times 10^{-4} C/m$
  4. $7.04\times 10^{-4} C/m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Torque is given by p x E. First, calculate the dipole moment vector p = q * d, where d is the vector from -q to +q. Then compute the cross product with the electric field E.

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

The work done in rotating a dipole through ${ 180 }^{ \circ  }$ from electric field direction is :

  1. $pE$
  2. $2pE$
  3. $\cfrac { pE }{ 2 } $
  4. $Zero$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work done due to dipole $=W=-pE\cos\theta$ where $p=$ dipole moment, $E=$ electric field
Here, $W=W _{(180)}-W _{(0)}=(-pE\cos180)-(-pE\cos0)=pE+pE=2pE$
Ans: (B)

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole consists of two opposite charges each of magnitude $ 1.0 \mu C $ separated by a distance of 2.0 cm. the diople is placed in an external electric field of $ 1.0 \times  10^5 N/C $ the maximum torque on the dipole is:

  1. $ 0.2 \times 10^{-3} N-m $
  2. $ 1.0 \times 10^{-3} N-m $
  3. $ 2.0 \times 10^{-3} N-m $
  4. $ 4.0 \times 10^{-3} N-m $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Maximum torque is given by tau = pE, where p = q * d. Here, p = (1.0 * 10^-6 C) * (0.02 m) = 2.0 * 10^-8 C-m. Then, tau = (2.0 * 10^-8) * (1.0 * 10^5) = 2.0 * 10^-3 N-m.