Electrical capacitance

In this topic we will discuss about the Electrical capacitance and electrostatics of conductor,electrostatic shielding  , and the capacity of an isolated spherical conductor .

Electrostatics of conductor –

As we know a conductor is a substance through which electric charge can conduct from one point to another . But there is some important results regarding  electrostatics of conductor which are follows –

1. In electrostatic equilibrium , electric field is zero every where inside the conductor . Suppose a conductor ABCD is held in an external electric field of intensity E₀ as shown in figure , the free electrons in the conductor moves from AB to CD . As a result , some net negative charge appears on AB . and the produced electric field E_p , which opposes the flow of free electrons from AB to CD . since Ep = E₀ so net field inside the conductor is zero .

2. The electric field just outside the charged conductor is perpendicular to the surface of the conductor at every point .
3. Net charge in the interior of the conductor is zero .

According to Gauss’s law  ∫E.ds =q/ϵ₀ ];

since inside the conductor E=0

therefore q= 0 also ;

4. Electric field at the surface of the charged conductor is given as E = σ/ϵ₀ where σ is the surface charge density . and the surface charge density is different at different point for irregular shaped conductor .

ELECTROSTATIC SHIELDING –

 It is the phenomenon to protect a space or an object from external electric field by covering it by conducting substance . as we know electric field inside a conductor is zero hence when an object is placed inside the conductor then there is no electric field connected to the object which is inside the conductor .

Electrical capacitance –

Electrical capacitance of a conductor is the ability of the conductor to store electric charge in it.

When conductor given some charge then its potential increases . Let Q is the charge given to the conductor then its potential increases to V volt so , we can say,   Q α V  or , Q = CV ; where C is a constant called capacity of the conductor , we can write  capacity C = Q/V  , Using this expression we can write , capacity of a conductor is the ratio of charge given to the potential developed in the conductor i.e. C = Q/V ;

 

In another way we can define , electrical capacity of a conductor is numerically equal to the charge required to increase the potential by unit volt .      Its unit is farad (F)

Here 1 Farad =1 coulomb/1 volt and its dimension is [ M^-1L^-2T⁴A²]

CAPACITY OF AN ISOLATED SPHERICAL CONDUCTOR –

Suppose a conductor of radius ‘r’ with centre ‘O’ has given charge ‘Q’  then its potential increases by ‘V’ . here potential V= q/4∏ϵ₀r

As we know capacity C = Q/V = Q/( q/4∏ϵ₀r) Or. C = 4∏ϵ₀r  ; Here r is in meter and  C is in farad .

As we can see C α r i.e larger the radius of the sphere and larger will be capacity of the conducting sphere .

Using this formula we can find the capacity of the earth which is given as

C= 4×3.14 x(1/9×10⁹) x 6.4x 10⁶ = 711 x 10^-6F  or 711μF .

For next topic of electrostatics  which is parallel plate capacitor -click here –

Gauss’s law and proof of Gauss’s law .

In this topic we will learn Gauss’s law , derivation of gauss’s law , derivation of coulomb’s law using gauss’s law .

Before to know about Gauss’s law and proof of Gauss’s law student must know electrostatic flux , to read the notes on electrostatic flux click here-

Question in the examinations may be asked as –

state and prove Gauss’s law , using gauss’s law derive Coulomb’s law.

Gauss’s law in electrostatics –

According to Gauss for a closed surface total flux  in the free surface is 1/ϵ₀ times the total charge inside the closed surface.

To download the pdf of Gauss’s law and proof of Gauss’s law click here-

Electric flux and area vector

In this topic we will discuss about Electric flux and area vector .

question may be asked as what is electric flux ? write its unit and dimension.

Area vector and electric flux –

As we know area is a scaler quantity , but in some cases or in case of some problems area is taken as vector quantity . the direction of area is taken as the normal of the surface at a given point . The vector associated with every area element of a closed surface is taken to be in the direction of the outward drawn normal .

 

Electric flux – Electric flux over an area in an electric field is the total number of field line passes through that area normally .  It is denoted by ɸ its unit is Nm²C^-1 . And its dimension is  [M¹L³T^-3A^-1]. Electric flux is a scaler quantity.

The  number of electric field lines crossing this area is  proportional to field intensity E . Let electric field lines makes an angle ϴ with the area vector dS , and E is the electric field intensity , then we can write  dɸ =  E. (dS cosϴ ) [ since dScosϴ is the component of area vector normal to the surface ].

So ,  dɸ = E dS (With vector sign).

Or,  ɸ_E = ∫E dS cosϴ

To download the pdf of complete assignment related to Electric flux and area vector ( This pdf includes Gauss’s law and its applications). click here-

Equipotential surface and Relation between electrostatic field and potential

In this topic we will discuss about  Equipotential surface and relation between electrostatic field and potential also,  we will know about equipotential surface for different-different conditions  .

 Equipotential surface- It is the surface inside the electrostatic field, the electric potential at every point on that surface are same. For any charge configuration, equipotential surface through a point is normal to the electric field at that point.

Equipotential surfaces of a single point charge are concentric spherical surfaces centred at the charge .

To download the complete notes on the topic, Relation between electrostatic field and potential click here-Equi-potential surface and Relation between electric field and electric potential

Properties of equi-potential surfaces –

(i) No work is done in moving a test charge from one point to another point on the equi-potential surface .

(ii) Electric field is always normal to the equi-potential surface .

(iii) No two equi-potential surface can intersect each other .

(iv) Equi-potential surfaces is closer in the region of strong electric field and they are farther apart in the region of weak electric field .

To view the related video click on the link given below –

 To download the notes on Equipotential surfaces and relation between electric field and electric potential click here-

 

Electrostatic potential energy and electrostatic potential

In this topic we will discuss about Electrostatic potential energy and electrostatic potential also with potential difference , potential due to multiple charges and potential at a point due to electric dipole .

To download  pdf of complete topic click here-

Electrostatic potential energy –  Electrostatic potential energy of a charge in an electrostatic field is the amount of work done required to bring that charged body from infinity to that point .  Its unit is joule

Let a charge Q is placed at point O as shown in figure , we have to find the potential energy at point ‘p’ which is ‘r’ distance away from the point ‘O’  . ( derivation of this topic , link is given below)

 

To see the video for electrostatic potential energy and electrostatic potential click on the link given below-

Electrostatic potential – electrostatic potential at any point in a region of electrostatic field is the minimum work done required to carry a unit positive charge from infinity to that point .

We can write  electrostatic potential  V = U/q   i.e.  electrostatic potential is equal to potential energy per unit charge .  Its unit is J/C .   or JC^-1  or NmC^-1 and its dimension is [M¹L²T^-3A^-1]

( derivation of this topic , link is given  Above/below)

 

Electrostatic potential difference –  Electrostatic  potential  difference between two points is the amount of work done required to bring the unit positive charge from one point to another point .

( derivation of this topic , link is given  Above/below)

To view the video related to the topic potential difference and potential at a point due to multiple charges visit on the link given below-

Electrostatic potential  at a point due to dipole- ( derivation of this topic , link is given below) . Before to know about this topic students must have to know about electric dipole , to read about electric dipole click here- 

To view the video related to the topic electrostatic potential at a point due to a dipole visit to the link given below-

 

Electrostatic forces are conservative  are  conservative in nature i.e. electrostatic force is independent of path followed , it only depends on initial and final position of the charge particle in an electric field .

 TO download complete notes of Electrostatic potential energy click here-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Electric field at any point on the axis of a uniformly charged ring

This topic discuss about the Electric field at any point on the axis of a uniformly charged ring .

Before to read this topic students need to know about electric field and charge density.To know about these topics click here-

Expression for the electric field intensity at a point on the axis of the charged ring –

Question may be asked as ; A charge is distributed uniformly over a ring  of radius ‘a’ . Obtain an expression for the electric field intensity E at a point on the axis of the ring. Hence show that for points at large distance from the ring behaves like a point charge.

Suppose a uniform circular ring of radius ‘a’ charged uniformly ‘Q’ which is distributed uniformly over the ring.

Suppose a small element ‘dl’ on the ring then, charge on the element is given by – dQ = (Q/2∏a) dl

The electric field at point p due to this element is given by  –

*****At the place of ∑ students can use integration with limit 0 to 2∏a ( in both case answer will be same ) *****

The field E is directed along the axis OP of the charged ring .

If r >> a , then the above expression may be written as ‘

E =  (Q/4∏ϵ₀ r² )  . This shows that for far points at long distance from the ring , it behaves like a point charge .

To view the video of this topic electric field at a pint on the axis of uniformly charged circular link click on the link given below-

Expression for torque and potential energy stored in dipole placed in uniform electric field

Before the study of this topic students must have to know about electric field and electric dipole  ;

To read electric field click here-

To read about electric dipole click here-

In this topic we will discuss about the , Expression for torque and potential energy stored in dipole placed in uniform electric field . and what will be Expression for torque and potential energy stored in dipole placed in non-uniform  electric field ?

Suppose an electric dipole  AB  having charges -q and +q are placed at distance 2a , and dipole  moment  ‘p’   is placed in an uniform electric field ‘E’ .

Then  Electrostatic force experienced on both the charges are  F = q E  , but the direction of forces on  each charges are opposite to each other . since the electric field E is constant then net force on the dipole will be zero ( since forces are in opposite directions ) .

Since the forces are equal , unlike and parallel acting at different points so , they form a couple . The couple tends to align the dipole axis along the direction of field ‘E’ .

Let’s draw AC perpendicular on electric field ‘E’ .

 To read or download complete notes on Expression for torque and potential energy stored in dipole placed in uniform electric field  click here-

But Questions may be asked by the students  that ,what will happen if electric field is not uniform ?

then its answer will be that the net force on the dipole will not be zero (0) . It means there will be translational and rotational motion  in the dipole . And net force will be equal to F1-F2 .

To view the video based on this topic torque and potential energy on the dipole placed in uniform electric field go to the link given below-

 

Electric dipole , electric field at a point on axial and equatorial line due to a dipole

In this assignment we will discuss about Electric dipole , electric field at a point on axial and equatorial line due to a dipole and dipole moment.

 

Before to read about electric dipole students must have to know about electric field .

To read  or download complete assignment of electric field click here

 

Electric dipole –  An electric dipole consist of a pair of equal and opposite point charges separated by small distance .

Let two charges of equal magnitude but opposite sign( q and -q)  are separated by distance 2a , then the arrangement is known as electric dipole .

Dipole moment  (p) – Dipole moment of an electric dipole is the measurement of the strength of the electric dipole  its magnitude is the product of magnitude of either charge and separation between them .

i.e.    Magnetic moment  p  = q ( 2a  )

Direction of magnetic field is given as  negative to positive charge i.e. -q to +q  ;

Its   SI  unit is  C-m ( coulomb meter ) and dimension is [M⁰ L¹ T¹ A¹ ] :

** Dipole field – It is the space around the dipole in which electric effect of the dipole can be experienced .  For electric dipole electric field E  α   1/r³  but for a point charge  E α 1/r²

In the link given below , students can find the notes related to  electric field at a point on axial and equatorial line due to a dipole.

 TO download complete assignment on Electric dipole , electric field at a point on axial and equatorial line due to a dipole – click here

To see the video of electric field at axial point due to a dipole click on the link given below 

To view the video related to the topic electric field at equatorial point of a dipole click on link given below

 

Electric field intensity at any point due to a short electric dipole , it explain the electric field due to a dipole at any point and using this derivation we can find the electric field at axial and equatorial point of a dipole .

 To download the assignment on Electric field intensity at any point due to a short electric dipole- click here

To view the video related to the topic electric field at any point due to dipole click  on the link given below

It is necessary for the students to get command on the above topic students has to solve some numerical base on this topic .

To solve the numerical based on this topic click here

Electric field and electric field lines

In this topic we will discuss about what is electric field and electric field lines , also electric field intensity at a point due to a point charge .

Electric field – Due to given  electric charge it is the  space around a charge particle in which electrostatic force can be experienced .

Electric field intensity –  Electric field intensity at a point is the force experienced at unit charge  placed at that point  , it is strength of electric field at that point .

Electric field   = F/q₀

Electric field intensity due to a point charge –  Suppose a charge Q is placed at point O , we have to find the electric field intensity at point p which is r distance away from charge Q   .

Suppose a test charge q is placed at point p , then force acting at charge q due to Q is given as                                             F = KQq/r²    ,

therefore electric field E = F/q

so, E =( kQq/r² )/q

E = kQ/r²

If we have to find the electric field at a point due to group of charges then we can write

Net electric field,  E = E1 + E2 +E3 ..………..

 

Electric field lines – It is the imaginary line the tangent at any point on this lines gives the direction of force at that point .

 To download complete assignment of this topic Electric field and electric lines of force click here-

To watch the video on electric field and electric field lines visit on given link below-

 

Properties of Electric field lines –

1. Electric field lines are continuous curve . They start from positive charge and end into negative charge . this is why electric field lines not form a closed loop . If there is a single charge then field lines start from the charge and goes into infinity .

      2. Tangent to the electric field lines at any point gives the               direction of electric field intensity at that point .

       3. No two field lines intersect each other . This is because at the point of intersection , there will be two direction of force at the same point which is not possible .

4. The electric field lines are always normal to the surface of a conductor .

        5. Where field lines are denser the electric filed intensity is more and vice- versa .

To watch the video of properties of electric field lines click on given link below-

***So in the form of electric field lines electric field intensity is equal to the number of field lines crossing normally a unit area around that point .

To download  the complete assignment of Electric field and electric field lines click here-

To solve the numerical based on this topic click here