Tag: electric charges and fields

Questions Related to electric charges and fields

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. $Zero$

Show answer
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 $

Show answer
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)

Show answer
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  } $
${ \left( { U } _{ p } \right)  } _{ minimum }=-pE$
$\theta ={ 0 }^{ o }$

An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a 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 p. E

  2. zero and minimum

  3. q. E and maximum

  4. 2q. E and minimum

Show answer
Correct Option: B
Explanation:

$F = p\dfrac{dE} {dr} = 0 \left ( \because E = constant \right )$
$u = -\overrightarrow{p} \overrightarrow{E} = -PE \left ( minimum \right )$

Intensity of an electric field (E) depends on distance $r$. In case of dipole, it is related as :

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

  1. $ E \propto \cfrac{1}{r}$

  2. $ E \propto \cfrac{1}{r^{2}}$

  3. $ E \propto \cfrac{1}{r^{3}}$

  4. $ E \propto \cfrac{1}{r^{4}}$

Show answer
Correct Option: C
Explanation:

Intensity of electric field due to a Dipole
$ E = \cfrac{p}{4\pi \varepsilon _{0}r^{3}} \sqrt{3cos^{2 }\theta+1}\Rightarrow E \propto \cfrac{1}{r^{3}}$

So, we can just dimensionally tell that Electric field will be inversely proportional to third power of $r$.

A point charge $Q$ lies on the perpendicular bisector of an electric dipole of dipole $p$. If the distance of $Q$ from the dipole is $r$ (much larger than the size of the dipole).then the electric field at $\theta$ is proportional to :

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

  1. $P^{2}$ and $r^{-3}$

  2. $P$ and $r^{-2}$

  3. $P^{-1}$ and $r^{-2}$

  4. $P$ and $r^{-3}$

Show answer
Correct Option: D
Explanation:

$\begin{array}{l} As\, \, we\, \, have, \ if\, \, r>1 \ { P _{ axi } }=\frac { 1 }{ { 4\pi { E _{ 0 } } } } \frac { { 2P } }{ { { r^{ 3 } } } }  \ { V _{ axi } }=\frac { 1 }{ { 4\pi { E _{ 0 } } } } \frac { P }{ { { r^{ 2 } } } }  \ Where\, \, in, \ Angle\, \, between\, \, { P _{ axi } }\, \, and\, \, P\, \, is\, 0. \ { E _{ equatorial } }=\frac { { kp } }{ { { r^{ 3 } } } }  \ i.e\, \, \, E\propto p \ and\, \, P\propto { r^{ -3 } } \end{array}$

Hence, Option $D$ is correct answer.

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.

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

  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

Show answer
Correct Option: A
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 } $