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Equipotential Lines And Equipotential Surfaces

Q: Two charges \$2\mu C\$ and \$-2\mu C\$ are placed at points A and B 6 cm apart.(a) Identify an equipotential surface of the system.(b) What is the direction of the electric field at every point on this surface?

(a) An equipotential surface is the plane on which total potential is zero.It is at the midpoint of the line AB and perpendicular to it.(b) The direction of the electric field at every point on this surface is normal to the plane in direction of AB.

Q: Angle between an equipotential surface and electric lines of force is :

The angle between Electric field and an equi-potential surface is always \$90^0\$. This is because,when the potential becomes constant,the negative potential gradient also becomes zero,hence necessitating the need for Electric field to be always normal with surface.

Q: Equipotential surfaces are shown in fig, then the electric field strength will be

Using\$,\$ \$dV = - \overrightarrow E \cdot \overrightarrow {dr} \$\$\Delta V = - E \cdot \Delta rcs\theta \$\$E = \frac{{ - \Delta V}}{{\Delta r\cos \theta }}\$\$E = \frac{{ - \left( { - 20 - 10} \right)}}{{10 \times {{10}^{ - 2}}\cos {{120}^0}}} = \frac{{ - 10}}{{10 \times {{10}^{ - 2}}\left( { - \sin {{30}^0}} \right)}} = \frac{{ - {{10}^2}}}{{ - 1/2}} = 200\,V/m\$direction of \$E\$ be perpendicular to the equipotential surface \$i.e.,\$ at \${120^0}\$ with \$x-\$ axis\$.\$Hence,option \$(C)\$ is correct answer.

Q: Two point charges +9q and +q are kept 16 cm apart. Where should a third charge Q be placed between them so that the system remains in equilibrium ?

Two point charges \$+9q\$ and \$+9\$. Kept apart \$=16cm=16\times { 10 }^{ -2 }m\$Two cases will be needed.Given charges, \$+q\$, \$+9q\$. let, the third charge \$q\$ be placed at a distance \$x\$ from \$q\$ and hence its distance from \$9q\$ and \$(16-x)cm\$ for the system to remain in equilibrium \${ F }_{ 1 }={ F }_{ 2 }\$Therefore, \${ F }_{ 1 }=\dfrac { K\left( q\times Q \right) }{ { x }^{ 2 } } \$\${ F }_{ 2 }=\dfrac { K\left( 9q\times Q \right) }{ { \left( 16-x \right) }^{ 2 } } \$Equating \${ F }_{ 1 }\$ and \${ F }_{ 2 }\$ we get,\$\dfrac { 9 }{ { x }^{ 2 } } =\dfrac { 1 }{ { \left( 16-x \right) }^{ 2 } } \$\${ F }_{ 1 }={ F }_{ 2 }\$or, \$\dfrac { K\left( q\times Q \right) }{ { x }^{ 2 } } =\dfrac { K\left( 9q\times Q \right) }{ { \left( 16-x \right) }^{ 2 } } \$or, \$\dfrac { 1 }{ { x }^{ 2 } } =\dfrac { 9 }{ { \left( 16-x \right) }^{ 2 } } \$or, \$\dfrac { 1 }{ x } =\dfrac { 9 }{ \left( 16-x \right) } \$or, \$16-x=3x\$or, \$4x=16\$or, \$x=4\$\$\therefore\$ \$(16-4)cm=12cm\$ from \$+9q\$.

Q: What is the equipotential surface? Draw the equipotential surface due to point charge.

Equipotential SurfaceThe surface in an electric field where the value of electric potential is the same at all the points on the surface is called equipotential surface. The potential difference between two points in an equipotential surface is zero. Thus, work done in moving the charge from one point to another in an equipotential surface is zero. since the work is done is zero when the direction of force (electric field) and displacement is normal. Thus, electric field is perpendicular to the plane in an equipotential surface. It is to be noted for the equipotential surface:1. For a uniform electric field \$ \vec{E} \$, the equipotential surface is normal to its field lines. According to figure 3.8,1(a) II and III are equipotential surfaces.2. For an isolated point charge:Potential at a distance r due to point charge \$ +\mathrm{q} \$\$V=\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{q}{r}\$If we draw a sphere of radius r surrounding the \$ + \$ q charge. Then, potential will be same at all points on the sphere i.e., equipotential surfaces are spherical whose charge is at the centre. For a positive point charge, as the radius of the spherical surface increases, the potential of spherical surface decreases.3. Equipotential surface for an electric dipole: The equipotential surface for an electric dipole are shown dotted in figure 3.8 ( \$ \mathrm{c} \$ ).4. Equipotential surfaces for a pair of similar point charges: The equipotential surface is as shown in figure\$ 3.8(\mathrm{d}) \$

Q: Define equipotential surface.

Any surface over which the potential is constant is called an equipotential surface.In other words, the potential difference between any two points on an equipotential surface is zero.Some important properties of equipotential surfaces :1. Work done in moving a charge over an equipotential surface is zero.2. The electric field is always perpendicular to an equipotential surface.3. The spacing between equipotential surfaces enables us to identify regions of strong and weak fields.4. Two equipotential surfaces can never intersect. If two equipotential surfaces could intersect, then at the point of intersection there would be two values of electric potential which is not possible.

Q: Depict the equipotential surfaces for a sytem of two identical positive point charges placed a distance 'd' apart.

Equipotential surfaces due to two identical charges is shown in figure.For two same charges the charges will repeal each other at a distance 'd' forming equipotencial surfaces.

Q: Two small spheres each carrying a charge q are placed r metre apart. If one of the spheres is taken around the other one in a circular path, the work done will be equal to :

Potential energy between any two given particles\$=\cfrac{kq_1q_2}{r}\$since revolving in circle does not change the distance \$r\$ between these charges, change in P.E. will be equal to zerohence \$work\$ \$done=0\$

Q: Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately:

A collection of charge located at a very large distance can b considered as the point charge. Now the equipotential surface for a point charge will have the same distance from the point in all the directions.Therefore, the euipotential points for a point charge will have a spherical surface.So, Option \$A\$ is correct.

Q: In a region of constant potential:

In a region of constant potential\$E=-\cfrac { dV }{ dr } =0\$ (\$\because\$ \$V=\$ constant)i.e., electric field is zero, so there can be no charge inside the region.

Physics

diagram

Gravitational Equipotential Surface

Gravitational equipotential surface is the locus of points which are at the same potential. Electric field in a space is always perpendicular to the equipotential surfaces and zero along the plane of equipotential surfaces.
Example:
For a point charge,

V = \frac{Q}{4 π ε _{o} R}

V =

constant,

⟹ R =

constant.
Hence for a point charge, equipotential surfaces are concentric spheres centered at the point charge.

definition

Equipotential surfaces

Surfaces having same potential are termed as equipotential surfaces
The properties of equipotential surfaces can be summarized as follows:

The electric field lines are normal to the equipotentials and are directed from higher to lower potentials.
By symmetry, the equipotential surfaces produced by a point charge form a family of concentric spheres, and for a constant electric field, a family of planes normal to the field lines.
The tangential component of the electric field along the equipotential surface is zero, otherwise non-vanishing work would be done to move a charge from one point on the surface to the other.
Work done in moving a particle along an equipotential surface is zero.

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Equipotential Surface of Various Charge System - I

10 mins

Equipotential Surface of Various Charge System - II

12 mins

Quick Summary With Stories

Equipotential surface and its properties

2 mins

Equipotential Surface of Various Charge System

3 mins

Important Questions

Two charges $2 μ C$ and $- 2 μ C$ are placed at points A and B 6 cm apart.
(a) Identify an equipotential surface of the system.
(b) What is the direction of the electric field at every point on this surface?

Medium

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Angle between an equipotential surface and electric lines of force is :

Easy

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Equipotential surfaces are shown in fig, then the electric field strength will be

Medium

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Two point charges +9q and +q are kept 16 cm apart. Where should a third charge Q be placed between them so that the system remains in equilibrium ?

Medium

View solution

What is the equipotential surface? Draw the equipotential surface due to point charge.

Medium

View solution

Define equipotential surface.

Medium

View solution

Depict the equipotential surfaces for a sytem of two identical positive point charges placed a distance 'd' apart.

Easy

View solution

Two small spheres each carrying a charge q are placed r metre apart. If one of the spheres is taken around the other one in a circular path, the work done will be equal to :

Medium

View solution

Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately:

Medium

View solution

In a region of constant potential:

Medium

View solution

diagram

Gravitational Equipotential Surface

definition

Equipotential surfaces

Quick Summary With Stories

Equipotential surface and its properties

Equipotential Surface of Various Charge System

Two charges 2μC and −2μC are placed at points A and B 6 cm apart.(a) Identify an equipotential surface of the system.(b) What is the direction of the electric field at every point on this surface?

Angle between an equipotential surface and electric lines of force is :

Equipotential surfaces are shown in fig, then the electric field strength will be

Two point charges +9q and +q are kept 16 cm apart. Where should a third charge Q be placed between them so that the system remains in equilibrium ?

What is the equipotential surface? Draw the equipotential surface due to point charge.

Define equipotential surface.

Depict the equipotential surfaces for a sytem of two identical positive point charges placed a distance 'd' apart.

Two small spheres each carrying a charge q are placed r metre apart. If one of the spheres is taken around the other one in a circular path, the work done will be equal to :

Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately:

In a region of constant potential:

Two charges $2 μ C$ and $- 2 μ C$ are placed at points A and B 6 cm apart.
(a) Identify an equipotential surface of the system.
(b) What is the direction of the electric field at every point on this surface?