Tag: electric charges and fields

Questions Related to electric charges and fields

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

physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. $-2\sqrt{3}J$

  2. $5\sqrt{3}J$

  3. $-2\sqrt {2}J$

  4. $3\sqrt {5}$

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Correct Option: A
Explanation:

Here length of dipole $2a=20cm=20\times { 10 }^{ -2 }m$, Charge $q=\pm 3\times { 10 }^{ -3 }C,\theta ={ 60 }^{ o }\quad $ and torque $\tau =6Nm$
As $\tau =pE\sin { \theta  } $
or $E=\cfrac { \tau  }{ p\sin { \theta  }  } =\cfrac { \tau  }{ q(2a)\sin { \theta  }  } \left( \because p=q(2a) \right) $
$\therefore E=\cfrac { 6 }{ 3\times { 10 }^{ -3 }\times 20\times { 10 }^{ -2 }\times \sin { { 60 }^{ o } }  } =\cfrac { { 10 }^{ 5 } }{ 5\sqrt { 3 }  } N{ C }^{ -1 }$
Potential energy of dipole $U=-pE\cos{\theta}=-q(2a)E\cos{\theta}$
$=-3\times { 10 }^{ -3 }\left( 20\times { 10 }^{ -2 } \right) \cfrac { { 10 }^{ 5 } }{ 5\sqrt { 3 } } \cos { { 60 }^{ o } } =\cfrac { -3\times { 10 }^{ -5 }\times 20\times { 10 }^{ 5 } }{ 5\sqrt { 3 } \times 2 } =-2\sqrt { 3 } J\quad \quad $

An electric dipole has the magnitude of its charge as $q$ and its dipole moment is $p$. It is placed in uniform electric field $E$. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively

physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. $q.E$ and max

  2. $2q.E$ and min.

  3. $q.E$ and min

  4. zero and min.

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Correct Option: D
Explanation:

When the dipole is in the direction of field then net force is $qE+(-qE)=0$
and its potential energy is minimum $=-p.E$
$=-qaE$

An electric dipole of diploe moment $\overrightarrow { p } $ placed in uniform electric field $\overrightarrow { E } $ has minimum potential energy when angle between $\overrightarrow { p } $ and $\overrightarrow { E } $

physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. $\cfrac{\pi}{2}$

  2. zero

  3. $\pi$

  4. $\cfrac{3\pi}{2}$

Show answer
Correct Option: C
Explanation:

Potential Energy=$ -PE \cos {\theta}$

when 
$ \theta=0 $
Potential Energy=$ -PE $
When
$ \theta=180 $
Potential Energy=$ +PE $
So, Maximum Potential Energy=$ +PE $ at angle $\theta=\pi$

 Two small electric dipoles each of dipole moment pi are situated at $(0, 0, 0)$ and $(r, 0, 0)$. the electric potential at a point $\left( \frac { r } { 2 } , \frac { \sqrt { 3 } r } { 2 } , 0 \right)$ is:

physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. $\frac { p } { 4 \pi \in _ { 0 } r ^ { 2 } }$

  2. $0$

  3. $\frac { p } { 2 \pi \epsilon _ { 0 } r ^ { 2 } }$

  4. $\frac { p } { 8 \pi \epsilon _ { 0 } r ^ { 2 } }$

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Correct Option: D

Potential at any point in the electric field produced by a dipole is

physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. $\infty , r$

  2. $\alpha r ^ { 2 }$

  3. $\frac { 1 } { r }$

  4. $\frac { 1 } { r ^ { 2 } }$

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Correct Option: A

A dipole of dipole moment $\overline {\text{p}} $ i s aligned at right angle to electrictric field $\overline {\text{E}} $ . To set it at an angle $\theta $ with E the amount of work done is


physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. $ - {\text{pEcos}}\theta $

  2. $ {\text{pEsin}}\theta $

  3. $ - {\text{pE}}\left( {{\text{sin}}\theta - 1} \right)$

  4. $ - {\text{pE}}\left( {{\text{sin}}\theta + 1} \right)$

Show answer
Correct Option: A

A electric dipole moment $\vec { p } =\left( 2.0\hat { i } +3.0\hat { j }  \right) \mu C.m$ is placed in a uniform electric field $\vec { E } =\left( 3.0\hat { i } +2.0\hat { k }  \right) \times { 10 }^{ 5 }N{ C }^{ -1 }$

physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. The torque that $\vec { E }$ exerts on $\vec { p }$ is $\left( 0.6\hat { i } -0.4\hat { j } -0.9\hat { k } \right) Nm$

  2. The potential energy of the dipole is $-0.6J$

  3. The potential energy of the dipole is $0.6J$

  4. If the dipole is free to rotate in the electric field, the maximum magnitude of potential energy of the dipole during the rotation is $1.3J$

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Correct Option: A,B,D
Explanation:

$\vec P = (2 \widehat i + 3 \widehat j) \mu cm$.
$\vec E = (0.3 \widehat i + 0.2 \widehat k) N \mu C^{-1}$
$\vec C = \vec P \times \vec E$
$=\begin{vmatrix}\widehat i & \widehat j & \widehat k\ 2 & 3 & 0\0.3  & 0 & 0.2\end{vmatrix}$
$= \widehat i (0.6) - \widehat (0.4) + \widehat k (-0.9)$
$= 0.6 \widehat i - 0.4 \widehat j - 0.9 \widehat k$
$U =- \vec P \cdot \vec E$
$=- (2 \widehat i + 3 \widehat j) \cdot (0.3 \widehat i + 0.2 \widehat k)$
$=- 0.6 J$
Consider,
the dipole rotated by 180$^o$.

The magnitude of dipole moment will not change only its direction will change.
$\therefore U=-\vec{P}.\vec{E}=|P||E|\ Sin\theta$
the max value of U is $|P||E|$
$=\sqrt{13} \times 10^{-6} \times \sqrt{13} \times 10^5
= 1.3 J.$
This is the maximum potential energy of the dipole.

 An electric dipole of moment $P$ is placed in the position of stable equilibrium in uniform electric field of intensity $E$. It is rotated through an angle $\theta$ from the initial position. The potential energy of electric dipole in the position is

physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. $\mathrm { pE } \cos \theta$

  2. $\mathrm { pE } \sin \theta$

  3. $\mathrm { pE } ( 1 - \cos \theta )$

  4. $\mathrm {- pE } \cos \theta$

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Correct Option: C

 A small dipole is placed is located at the center of an imaginary spherical Gaussian surface (radius R) with its dipole moment in +X-direction . Let $E _{max}$ & $E _{min}$  be maximum & maximum possible magnitude of field over the surface. 
Statement 1:   Number of points where E = $E _{max}$ is infinite.
Statement 2:    Number of points where E = $E _{min}$ is two.

physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. Both 1 and 2 are correct

  2. Both 1 and 2 are incorrect

  3. Only 1 is correct

  4. Only 2 is correct

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Correct Option: C

If $ P= 2 \times 10^7 cm $ of an electric dipole placed in an uniform electric field of intensity $ 1 \times  10^8 N/C $ making an angle $ 60^0 $  with electric field. find magnitude of potential energy____J?

physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

  1. $ 10^{-3} $

  2. $ 10^{-4} $

  3. $ 1.73 \times 10^{13} $

  4. $ 10^{2} $

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Correct Option: C