Questions Related to physics

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

An electric dipole placed with its axis in the direction of a uniform electric field experiences:

  1. a force but not torque

  2. a torque but no force

  3. a force as well as a torque

  4. neither a force nor a torque

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

Total force of on diopole $= E\ q +E( -q )$ $= 0$
We know,
 Torque $= \vec{P} \times \vec{E}$
but axis of dipole is in the direction of electric field
$\therefore \tau = P.E\ sin\ 0$
$\therefore \tau = 0$
$\therefore $ No torque, No force is acting on dipole

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

An electric dipole of momentum $3 \times {10}^{-8}\ Cm$ is placed in an electric field of $6 \times {10}^{4}\ N/C$ with is axis making an angle of $30^o$ with the field . Find the torque acting on the dipole.

  1. $ (9 \times 10^{-5} )N-m$
  2. $ (9 \times 10^{-4} )N-m$
  3. $ (9 \times 10^{-3} )N-m$
  4. $ (90 \times 10^{-8} )N-m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that Torque $(\vec \tau) = \vec p \times \vec E$


$  \tau = pE\sin \theta$
$ = (3\times 10^{-8})\times ( 6\times 10^4) \sin30^0$
$ = (9 \times 10^{-4} )N-m$

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.