Tag: physics

Questions Related to physics

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

An electric dipole consists of two opposite charges each of magnitude $2\mu C$ separated by a distance $1cm$. The dipole is placed in an external field of $10^3N/C$. The maximum torque on the dipole is

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

  1. $1\times 10^{-5}N-m$

  2. $2\times 10^{-5}N-m$

  3. $0.5\times 10^{-5}N-m$

  4. $Zero$

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Correct Option: B

The relation connecting the energy U and distance r between dipole and induced dipole is :

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

  1. $U\propto r$

  2. $U\propto r^{2}$

  3. $U\propto r^{-6}$

  4. $U\propto r^{6}$

Show answer
Correct Option: C
Explanation:

The potential energy for the dipole-dipole interaction is given by $\displaystyle U=-\dfrac{2p _1^2p _2^2}{3(4\pi\epsilon _0)^2k _BT r^6}$
thus, $U \propto r^{-6}$

Carbon tetrachloride has zero dipole moment because of ________.

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

  1. planar structure

  2. Smaller size of C and Cl atoms

  3. regular tetrahedral structure

  4. none of these

Show answer
Correct Option: C
Explanation:

Carbon tetrachloride molecule has zero dipole moment even though C and Cl have different electronegativities and each of the C - Cl bond is polar and has some dipole moment. This is because the individual dipole moments cancel out because of the symmetrical tetrahedral shape of the molecule.



An electric dipole moment $ \overrightarrow { P }  $ is lying a uniform electric field $ \overrightarrow { E }  $ .The work done in rotation the dipole by $ 37^o $

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

  1. $ \dfrac {2}{5} PE $

  2. $ - \dfrac {2}{5} PE $

  3. $ \dfrac {PE}{5} $

  4. $ \dfrac {3}{5} PE $

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Correct Option: C

An electric dipole is placed in an electric field generated by a point charge then

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

  1. Then net electric force on the dipole must be zero

  2. The net electric force on the dipole may be zero

  3. The torque on the dipole due to the field may be zero

  4. Both (2) and (3)

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Correct Option: C

An electric dipole when placed in a uniform electric field $E$ will have a minimum potential energy if the dipole moment makes the following angle with $E$

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

  1. $\pi$

  2. $\pi /2$

  3. zero

  4. $3\pi /2$

Show answer
Correct Option: C
Explanation:

${ U } _{ p }=-p\bullet E=-pE\cos { \theta  } $
${ \left( { U } _{ p } \right)  } _{ minimum }=-pE$
$\theta ={ 0 }^{ o }$${ U } _{ p }=-p\bullet E=-pE\cos { \theta  } $
${ \left( { U } _{ p } \right)  } _{ minimum }=-pE$
$\theta ={ 0 }^{ o }$