Q: The electric potential at a point on the axis of an electric dipole depends on the distance \$r\$ of the point from the dipole as

The expression of electric potential for dipole is , \$V=\dfrac{1}{4\pi\epsilon_0} \dfrac{p\cos\theta}{r^2}\$ where \$p=qd\$ dipole moment. so,\$ V \propto \dfrac{1}{r^2} \$ Ans:(B)

Q: The electric potential at a point on the equatorial line of an electric dipole is

\$\textbf{Step 1: Electric potential at P due to dipole}\$\$\textbf{[Refer Fig.]}\$Let OP be equatorial line.Let \$r\$ be the distance of each charge from point P Potential due to charge \$q\$ at point \$P, V_1 = \dfrac {kq}{r}\$ Potential due to charge \$-q\$ at point \$P , V_2= \dfrac {-kq}{r}\$\$\textbf{Step 2: Total potential at point P}\$ \$V = V_{1} + V_{2}\$ \$\Rightarrow V = \dfrac {kq}{r} - \dfrac {kq}{r} = 0\$Hence, the net potential at a point on the equatorial line of an electric dipole is zero.Hence, Option (D) is correct.

Q: An electric field of \$1000\$V/m is applied to an electric dipole at angle of \$45^o\$. The value of electric dipole moment is \$10^{-29}\$C.m. What is the potential energy of the electric dipole?

\$U=-\vec{P}\cdot \vec{E}\$\$=-PE\cos\theta\$\$=-(10^{-29})(10^3)\cos 45^o\$\$=-0.707\times 10^{-26}\$J\$=-7\times 10^{-27}\$J.

Q: The electric potential due to an extremely short dipole at a distance r from it is proportional to :

Potential at point \$P= \dfrac{KV}{r_1}-\dfrac{KV}{r_2}\$\$V= KV(\dfrac{r_2-r_1}{r_1r_2})\$we are taking extremely short dipole \$r_1 \underline {\simeq} r_2= r\$\$r_2-r_1 \underline {\simeq} d\ cos \theta \$\$V= \dfrac{KV\ d\ cos\ theta}{r^2}\$\$V= \dfrac{K\ P\ cos\ theta}{r^2}\$ \$ P = V d \$, where P is the dipole moment.\$\therefore V \propto \dfrac{1}{r^2}\$

Q: An electric dipole is along a uniform electric field If it is deflected by \$60 ^ { \circ } ,\$ work done by agent is\$2 \times 10 ^ { - 19 } \mathrm { J }\$ . Then the work done by an agent if it is isdeflected by \$30 ^ { \circ }\$ further is

Working on electric dipole when deflected by an angle of \${60^0}\$ is given by\$,\$\${W_1} = U = - PE\cos {60^0} = - 2 \times {10^{ - 19}}J.\$Now\$,\$ work done in deflecting he dipole by another \${30^0}\$ is given by\$,\$\${W_1} = - PE\cos {90^0} = 0\$Therefore work done by the agency which deflected dipole by \${30^0}\$ mpore is\$,\$\$W = {W_2} - {W_1} = 0 - \left( { - 2 \times {{10}^{ - 19}}} \right) = 2 \times {10^{ - 19}}J.\$ Hence,option \$(B)\$ is correct answer.

Question 1

The electric potential at a point on the axis of an electric dipole depends on the distance $r$ of the point from the dipole as

Accepted Answer

&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;&#10;The expression of&#10;electric potential for dipole is , $V=\dfrac{1}{4\pi\epsilon_0} \dfrac{p\cos\theta}{r^2}$&#10;where $p=qd$ dipole moment.&#10;&#10;so,$ V \propto \dfrac{1}{r^2} $&#10;&#10;Ans:(B)&#10;&#10;

Question 2

Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

Accepted Answer

Dipole consist of two charges of opposite nature and the same magnitude having a small distance between them. The axis between the two dipoles, perpendicular to the plane, is where the potential due to the dipole is zero (straight line joining the arrows between the two dipoles).

Question 3

A sphere encloses an electric dipole within it. The total flux across the sphere is

Accepted Answer

The total electric flux coming out of the sphere is zero because the net charge enclosed by the surface is zero

Question 4

The value of electric potential at any point due to any electric dipole is:-

Accepted Answer

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Question 5

Two point dipoles of dipole moment $\vec {p}_{1}$ and $\vec {p}_{2}$ are at a distance $x$ from each other and $\vec {p}_{1}\parallel \vec {p}_{2}$. The force between the dipoles is

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Question 6

The electric potential at a point on the equatorial line of an electric dipole is

Accepted Answer

$\textbf{Step 1: Electric potential at P due to dipole}$$\textbf{[Refer Fig.]}$Let OP be equatorial line.Let $r$ be the distance of each charge from point P Potential due to charge $q$ at point $P, V_1 = \dfrac {kq}{r}$ Potential due to charge $-q$ at point $P , V_2= \dfrac {-kq}{r}$$\textbf{Step 2: Total potential at point P}$                 $V = V_{1} + V_{2}$                 $\Rightarrow V = \dfrac {kq}{r} - \dfrac {kq}{r} = 0$Hence, the net potential at a point on the equatorial line of an electric dipole is zero.Hence, Option (D) is correct.

Question 7

An electric field of $1000$V/m is applied to an electric dipole at angle of $45^o$. The value of electric dipole moment is $10^{-29}$C.m. What is the potential energy of the electric dipole?

Accepted Answer

$U=-\vec{P}\cdot \vec{E}$$=-PE\cos\theta$$=-(10^{-29})(10^3)\cos 45^o$$=-0.707\times 10^{-26}$J$=-7\times 10^{-27}$J.

Question 8

Potential due to an electric dipole is represented by:

(where $p$ is the dipole moment, $r (> > 2 a)$ is the distance at which the potential $V$ of the dipole is calculated and $θ$ is the angle between the distance vector and the dipole.)

Accepted Answer

We resolve the electric dipole into horizontal and vertical components as shown in the figure.Parallel component of electric field $E_{\parallel} = \dfrac{2p \cos\theta}{4\pi \epsilon_o r^3}$Perpendicular of electric field $E_{\perp} = \dfrac{p\sin \theta}{4\pi \epsilon_o r^3}$Potential due to dipole $V = -\int \vec{E_{\parallel}} .\vec{dr} - \int \vec{E_{\perp}}. \vec{dr}$Second term goes to zero as $\vec{E_{\perp}}$ is perpendicular to $\vec{dr}$.Thus potential due to dipole $V = -\dfrac{2p \cos\theta}{4\pi \epsilon_o } \int \dfrac{dr}{r^3}$Or  $V = -\dfrac{2p \cos\theta}{4\pi \epsilon_o } \times \dfrac{1}{(-2) r^2}$$\implies$ $V = \dfrac{p \cos\theta}{4\pi \epsilon_o r^2} $

Question 9

The electric potential due to an extremely short dipole at a distance r from it is proportional to :

Accepted Answer

Potential at point $P= \dfrac{KV}{r_1}-\dfrac{KV}{r_2}$$V= KV(\dfrac{r_2-r_1}{r_1r_2})$we are taking extremely short dipole $r_1 \underline {\simeq} r_2= r$$r_2-r_1 \underline {\simeq} d\ cos \theta $$V= \dfrac{KV\ d\ cos\ theta}{r^2}$$V= \dfrac{K\ P\ cos\ theta}{r^2}$    $ P = V d $, where P is the dipole moment.$\therefore V \propto \dfrac{1}{r^2}$

Question 10

An electric dipole is along a uniform electric field If it is deflected by $60 ^ { \circ } ,$ work done by agent is$2 \times 10 ^ { - 19 } \mathrm { J }$ . Then the work done by an agent if it is isdeflected by $30 ^ { \circ }$ further is

Accepted Answer

Working on electric dipole when deflected by an angle of ${60^0}$ is given by$,$${W_1} = U =  - PE\cos {60^0} =  - 2 \times {10^{ - 19}}J.$Now$,$ work done in deflecting he dipole by another ${30^0}$ is given by$,$${W_1} =  - PE\cos {90^0} = 0$Therefore work done by the agency which deflected dipole by ${30^0}$ mpore is$,$$W = {W_2} - {W_1} = 0 - \left( { - 2 \times {{10}^{ - 19}}} \right) = 2 \times {10^{ - 19}}J.$  Hence,option $(B)$ is correct answer.

Revise with Concepts

Potential Due to an Electric Dipole

Quick Summary With Stories

Potential due to Elelctric Dipole

Electric Field at the Equatorial point of a Dipole

The electric potential at a point on the axis of an electric dipole depends on the distance $r$ of the point from the dipole as

Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

A sphere encloses an electric dipole within it. The total flux across the sphere is

The value of electric potential at any point due to any electric dipole is:-

Two point dipoles of dipole moment $p_{1}$ and $p_{2}$ are at a distance $x$ from each other and $p_{1} ∥ p_{2}$ . The force between the dipoles is

The electric potential at a point on the equatorial line of an electric dipole is

An electric field of $1000$ V/m is applied to an electric dipole at angle of $4 5^{o}$ . The value of electric dipole moment is $1 0^{- 29}$ C.m. What is the potential energy of the electric dipole?

Potential due to an electric dipole is represented by:

(where $p$ is the dipole moment, $r (> > 2 a)$ is the distance at which the potential $V$ of the dipole is calculated and $θ$ is the angle between the distance vector and the dipole.)

The electric potential due to an extremely short dipole at a distance r from it is proportional to :

An electric dipole is along a uniform electric field If it is deflected by $6 0^{\circ},$ work done by agent is $2 \times 1 0^{- 19} J$ . Then the work done by an agent if it is isdeflected by $3 0^{\circ}$ further is

Revise with Concepts

Potential Due to an Electric Dipole

Quick Summary With Stories

Potential due to Elelctric Dipole

Electric Field at the Equatorial point of a Dipole

The electric potential at a point on the axis of an electric dipole depends on the distance r of the point from the dipole as

Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

A sphere encloses an electric dipole within it. The total flux across the sphere is

The value of electric potential at any point due to any electric dipole is:-

Two point dipoles of dipole moment p​1​ and p​2​ are at a distance x from each other and p​1​∥p​2​. The force between the dipoles is

The electric potential at a point on the equatorial line of an electric dipole is

An electric field of 1000V/m is applied to an electric dipole at angle of 45o. The value of electric dipole moment is 10−29C.m. What is the potential energy of the electric dipole?

Potential due to an electric dipole is represented by: (where p is the dipole moment, r(>>2a) is the distance at which the potential V of the dipole is calculated and θ is the angle between the distance vector and the dipole.)

The electric potential due to an extremely short dipole at a distance r from it is proportional to :

An electric dipole is along a uniform electric field If it is deflected by 60∘, work done by agent is2×10−19J . Then the work done by an agent if it is isdeflected by 30∘ further is

The electric potential at a point on the axis of an electric dipole depends on the distance $r$ of the point from the dipole as

Two point dipoles of dipole moment $p_{1}$ and $p_{2}$ are at a distance $x$ from each other and $p_{1} ∥ p_{2}$ . The force between the dipoles is

An electric field of $1000$ V/m is applied to an electric dipole at angle of $4 5^{o}$ . The value of electric dipole moment is $1 0^{- 29}$ C.m. What is the potential energy of the electric dipole?

Potential due to an electric dipole is represented by:

(where $p$ is the dipole moment, $r (> > 2 a)$ is the distance at which the potential $V$ of the dipole is calculated and $θ$ is the angle between the distance vector and the dipole.)

An electric dipole is along a uniform electric field If it is deflected by $6 0^{\circ},$ work done by agent is $2 \times 1 0^{- 19} J$ . Then the work done by an agent if it is isdeflected by $3 0^{\circ}$ further is