Electric Lines Of Force

An electric line of force is defined as the path traced by a test charge when placed in the electric field.

According to coulomb's Laws, a positive charge repels a positive charge and attracts a negative charge, therefore, an electric line of force always starts from the positive charge and ends on the negative charge.
                   

Properties of electric lines of force :Following are the important properties of electric lines of force :

1. An electric line of force starts from the positive charge and ends on the negative charge.

2. An electric line of force does not form a closed loop like a magnetic line of force. There is no electric field inside a charged body and, therefore, the electric line of force ends on the negative charge.
                                 
3. Two electric lines of force never cross each other. The crossing of two lines of force means that there are two directions of the force on a test charge at a point which is impossible.It is well known that a body can move in one and only one direction under the action of force. Hence two electric lines of force can never cross each other.

4. The electric lines of force in the same direction repel each other and those in the opposite direction attract each other.
                                 
5. The tendency of electric lines of force is to taken easy electric path.

Electric Field

An electric field is said to exist at a point if a test charge (unit positive charge) placed at that point experiences an electrical force.

Every charged body exhibits electric field : Theoretically, electric field extends up to infinity but its effect practically dies away very quickly as the distance from the charged body is increased. Therefore, the region where the influence of a charged body can be experienced is very limited and this region or space near the charged body is called electric field.
                                 

An electric field cannot be seen. Therefore, to visualize electric field pattern, we draw electric lines of force. Each electric line of force starts from positive charge and ends on the negative charge (as shown in fig.).

As a matter of fact, electric lines of force are imaginary lines drawn in the electric field. Thus in fig. above, the electric line of force is acting from left to right. This is also the direction of the electric field.
                                                                        ➝                   ➝  
Mathematically we can define electric field E as the force (F) acting per unit test charge  (qo)
                                             ➝    ➝
i.e.,                                        E = F/qo

SI unit of electric field is Newton per Coulomb (N/C), and we can also write the above equation as
                                                       ➝      ➝
                                                                F  = qo E
                   ➝  
Electric field (E) is a vector Quantity and for positive charge, its direction is 
                                             ➝  
towards the direction of  force (F) and for negative charge, its direction is opposite to the direction of force.

Electric Field is also called field intensity, field strength or electric field strength.

Electric field can also be defined as : It is the space around a charge in which the other charged body can experience the force of attraction or repulsion.


courtesy:en.wikipedia.org

Calculations Using Coulomb's Law

Calculations Using Coulomb's Law :

1. Determine the force between two charges, each of one coulomb when they are separated at one meter distance in air.

Solution: The magnitude of force between two charges is given by
F = (q1q2)/(4∏ϵoϵrd²)   N
q1  =  q2  =  1 coulomb
ϵo = absolute permittivity  =  8.854 x 10-12 F/m
ϵr = 1                                                                     [Medium is air]
d= distance between the charges = 1m

F= (1×1)/4∏×1×1×1×8.854 x 10-12


F =  9 x 109   N

2. An electron and a proton are at a distance of 10^{-9  m}  from each other in free space. compute the force between them.

Solution : The charge on an electron,    q1 = –1.6 × 10-19   C
and  the charge on proton,                   q2 = +  1.6 × 10-19   C

The force between the two charges is given as, 
      
                           F = (q1q2)/(4∏ϵoϵrd²)   N

ϵo = absolute permittivity  =  8.854 x 10-12 F/m
ϵr = 1
d = 10<sup>-9   m

 F =        (</sup> –)1.6 × 10-19   C  × (+ ) 1.6 × 10-19   C / 4∏×1×10^-9  ×10^-9  ×8.854 x 10-12
F = –23.04 × 10-11  N

The negative sign indicates that the force is of attraction .
For ease in calculations take the value of  1/ 4∏ϵo =   9 x 109 

3. The magnitude of two charges is doubled and distance of their separation is also doubled. Find the coulomb's force between them.

Solution :  F = Kq1q2/r² 
             
                   F = Kq1'q2'/R²

               q1' = 2q1

                       q2' = 2q2
                      
                R = 2r
                  =   K. (2q1)(2q2)/4r²
                  =   K. 4q1q2/ 4r² 
                         =    K. q1q2/ r² 
                          =    F.
Hence magnitude of coulomb's force will remain same.

 Check your understanding with Multiple choice Questions:

1. The law that governs the force between electric charges is called
(a) Ampere's Law                 (b) Coulomb's Law
(c) Faraday's Law                 (d) Ohm's Law

2. Which one of the following is the unit of electric charge ?
(a) Coulomb                        (b) Newton
(c) Volt                               (d) Coulomb/Volt 

3. When a conductor gets charged due too the mere presence of another body, the phenomenon is known as :
(a) friction                          (b) conduction
(c) induction                       (d) none of the above 

4. Whenever induction takes place, the positive induced charges is equal to :
(a) inducing charge            
(b) negative induced charge 
(c) negative induced charge and also equal to the inducing charge     
(d) none of the above

5. The distance between two charged bodies is halved, the force between them becomes :
(a) half                               (b) one fourth
(c) double                           (d) four times

6. The number of electrons in one coulomb of charge will be
(a) 5.46  ×  1029                  
(b) 6.25  × 1018 
(c)   1.6  ×   1019                
(d)      9  ×   1011 

7. The force between the electrons separated by a distance r varies as
(a) r²                                                                    (b) r ^-1
(c) r                                   (d) r ^-2

8. The coulomb's force between two charges
(a) follow inverse square law
(b) it is conserved
(c) it is vector quantity 
(d) it is additive in nature

9. Which of the following is not a property of electric charge ?
(a) It is discrete in nature
(b) It is conversed
(c) It is vector quantity
(d) It is addictive in nature

10. The magnitude of two charges is doubled and distance of their separation is also doubled. The electrostatic force between them will
(a) be halved                               (b) be doubled
(c) become four times                  (d) remains unchanged

11. Two charges are placed at a certain distance apart. A brass sheet is placed between them. The force between them will
(a) increase                                (b) decrease
(c) remains unchanged                (d) none of the above

12 Two point charges placed at a distance r in air is 10 N. if they are in a medium of relative permittivity 4, the force between them will be :
(a) r                                          (b) r/k
(c) r /√k                                    (d) r √k

13. Two balls carrying charges of + 3 µc and – 3 µc attract each other with a force F. If  charge + 3 µc  is added to both, the force between the balls will be :
(a)  4F                                       (b)  2F
(c)  F                                         (d) zero

14. Force between two charges, when placed in free space is 10 N. If they are in medium of relative permittivity 5, the force between them will be :
(a) 0.5 N                                    (b) 2 N
(c) 20 N                                     (d) 50 N

15. Force between two charges when placed in air is 10 N. If they are in a medium of relative permittivity 4, the force between them will be :
(a) 2 N                                       (b) 2.5 N
(c) 0.4 N                                     (d) 40 N

16. Two electrons are separated by distance 'r' mere and have a coulomb force equal to F. Two alpha particles separated by 2r meters will have force equal to
(a) 2 F                                        (b) 3 F
(c) F/2                                        (d)  F

17. The permittivity of the vacuum is:
(a) unity                                     (b) more than one
(c) less than one but not zero       (d) zero

18. If one of the two given charges is doubled and the distance between them is reduced to half, the coulomb force between them will increase by a factor of :
(a) 16                                        (b) 8
(c) 4                                          (d) 2

19. One coulomb is the point charge which when placed at one meter from an equal and similar point charge in vacuum repels it with a force :
(a)  9 x 109 dyne                       (b)  9 x 109 N 
(c)  1 dyne                                (d) 1 N

20. The value of 4∏ϵo    (in mks system) is : 
(a)   9 x 109                            (b) 1 / (9 x 109)
(c)   1                                     (d) 8.8 x 10-12 

Coulomb's Laws Of Electrostatics

Coulomb's Laws Of Electrostatics :

First Law : Like charges repel each other and unlike charges attract each other. In other words, bodies having same charges repel each other and bodies oppositely charged attract each other.

The first law tells only about the nature of force i.e., repulsive or attractive. It does not tell about the magnitude of force. The magnitude of the force between two charged bodies is given by the second law.

Second Law : The force of attraction or repulsion between two charges is directly proportional to the product of magnitude of the two charges and inversely proportional to the square of distance between them.

If two point charges Q₁ and Q_{2 have distance d between them, then force  F between the charges can be mathematically expressed as :}

                             F = K × Q1Q2/d²

Where K is a constant of proportionality and its value depends upon the medium in which the charges are placed and the system of units used. In SI units force is measured in newton, charge in coulomb, distance in meter and the value of K is given as:
                 
                             K = 1/4πϵoϵr           (in S.I. system)
where   
ϵo = Absolute Permittivity of vacuum or prematurity of free space
ϵr = Relative Permittivity of the medium w.r.t. vacuum in which the charges are placed.
The value of  ϵo  = 8.854 x 10-12  farad/metre and the value of ϵr is different for different media, for air ϵr = 1. The value of 1/4πϵo = 9 x 109


                                          F = K × Q1Q2/d²
                                       F = (1/4πϵoϵr)  × Q1Q2/d²
                                     F = Q1Q2/4πϵoϵrd^{2  (in N)}

Units.   In the formula,     F = Q1Q2/4πϵoϵrd²  
F is measured in newton, Q1,Q2 in coulomb, d in metre and  ϵo in farad/metre.

Unit Charge :

(i) S.I.System : By unit charge, we mean one coulomb charge. By coulomb's second law,
                       F = Q1Q2/4πϵoϵrd²  newton
                      F =  9 x 109   newton 
and          Q1, Q2 = Q
                      ϵr = 1
                      ϵo = 8.854 x 10-12 
                      d = 1m
Put everything in above relation,
             9 x 109 =  ( Q ×  Q ) / 4π ×  8.854 x 10-12 ×1 ×1
                 Q2   =   ± 1 coulomb
Hence unit charge or one coulomb charge in S.I.system can be defined as:-

A unit charge or One coulomb is that much charge which when placed at a distance of one meter from an equal and similar charge in air, is repelled with a force of 9 x 109 newton from it. 

(ii) In C.G.S System : Unit of charge is stat coulomb
                                1 coulomb =  3 x 109  stat coulomb

Electrostatics

Introduction To Electrostatics : The branch of physics which deals with the study of charges at rest is called electrostatics.

If a glass rod is rubbed with silk cloth, electrons pass from glass rod to silk cloth and the glass rod becomes positively charged while the silk piece attains an equal negative charge. Since glass rod and silk cloth are both insulators, they retain charges on them because electrons cannot move.

In other words, electricity on them is static or at rest and hence the process comes under the Electrostatics.

Explanation of Charges : The number of electrons in an atom is equal to the number of protons, therefore, atom is neutral as whole. A body consists of atoms, therefore, the body is neutral under ordinary conditions. 

However, if from such a neutral body, electrons are detached (by rubbing etc.), there occurs a deficit of electrons in the body. Consequently the body no longer remains neutral due to the shortage of electrons. The result is that the body attains positive charge.

When a body is short of its due share of electrons or there is deficit of electrons in the body it is said to be positively charged.

On the other hand, a negatively charged body has excess of electrons from its normal due share. If a neutral body is supplied with electron, the body loses its neutrality and attains a negative charge.

Therefore, a negatively charged body has excess of electrons from its normal due share.

Total deficiency or excess of electrons in a body is known as charge.

To give a negative charge to any body, extra electrons must be supplied to it. To supply these extra electrons, work will have to be done, which is stored in the body in the form of energy. This makes the charged body capable of doing work.

Units of Charge : The charge on an electron is so small that it is not possible and convenient to take it as the unit. In practice, the charge is measured in coulomb (C). One coulomb of charge is equal to the charge on 625 × 10¹⁶ electrons. i.e.

Charge of 1 coulomb = charge on 625 × 10¹⁶  electrons.

∴ Practical unit of charge is coulomb. And a smaller unit of charge is micro-coulomb is also used.

1 micro-coulomb (i.e. 1 µC) = 10⁻⁶ C coulomb.

Difference between Transverse Waves and Longitudinal Waves

Transverse waves

Longitudinal waves

1.       In transverse waves the particles of the medium vibrate in a direction at right angles to the direction of propagation of the wave. 2.       Transverse waves travel in the form of crests and troughs. One crest and one trough constitute a wave. 3.       Transverse waves are possible in media which possess the properties of elasticity of shape or they have  a free surface i.e., they are possible in solids and liquids. 4.       Transverse waves can be polarized. 5.       Transverse displacement travel with the wave but there is no change in pressure of medium. 6.       Transverse waves can be represented by sine curve directly. 7.       Examples : Waves in ropes, ripples on the surface of liquids and electromagnetic waves are transverse waves.

1.       In longitudinal waves the particles of the medium vibrate back and forth parallel to the direction of propagation of the wave. 2.       Longitudinal waves travel in the form of compressions and rarefactions. One compression and one rarefaction constitute one wave. 3.       Longitudinal waves are possible in media which possess the properties of elasticity of volume  i.e., they are possible in solids, liquids and gases but in gases, this is the only wave motion possible. 4.       Longitudinal waves can not be polarized. 5.       Pressure of medium changes when longitudinal displacement passes through it, but there is no transvere displacement in the medium. 6.       Longitudinal waves cannot be represented by sine curve directly. 7.       Examples : Sound waves in air, gases and waves in springs are longitudinal waves.

Microscope

A microscope is a device used to see small object much magnified at the least distance of distinct vision.

Least distance of distinct vision : The minimum distance from the eye at which the objects are clearly visible is called the least distance of distinct vision. It is denoted by D. For a normal eye it is about 25 cm.

The two types of microscopes are discussed below :
1. Simple microscope or magnifying glass,
2. Compound microscope

1. Simple microscope or Magnifying glass
The size of an object depends upon the angle subtended by the object at the eye. The angle subtended depends upon the dimensions of the object and its distance from the eye. If the object is  brought nearer, the angle subtended at the eye increases and the object appears bigger and more distinct. Thus to see san object distinctly, it should be moved very near to the eye. But if it is brought near the eye at a distance less than the least distance of distinct vision, it becomes indistinct. Thus to see the object distinctly, It should be moved very close to the eye but its image should be formed at the least distance of distinct vision.

An ordinary convex lens of small focal length kept close to the eye can be used as a simple microscope or magnifying glass.

Watch makers use a single convex lens to get a magnified view of the fine parts of the watch.

Magnifying Power : The magnifying power of a simple microscope is the ratio of the angle subtended at the eye by the image as seen through the lens to the angle subtended by the object at the unaided eye, when both are placed at the least distance of distinct vision, it is denoted by M.

The mathematical formula for Magnifying Power, M is

                                            M = D/u
            
                                               = 1+D/f

Where, D is the least distance of distinct vision and is equal to v.
D being constant, the magnifying power depends upon the focal length of the lens.
       Smaller the focal length, greater will be the magnifying power of the lens.

2. Compound microscope : The magnification produced by simple microscope is small and can only be increased by decreasing the focal length of the lens. But there is a practical limit to it. Large magnification can be obtained by using compound microscope in which magnification is obtained in two stages by using two convex lenses.

Magnifying Power : Magnifying power of the microscope is defined as the ratio of the angle subtended by the image at the eye as seen through the microscope to the angle subtended by object at the unaided eye when both are placed at the least distance of distinct vision.

The mathematical formula for Magnifying Power, M is       

fe = focal length of the eye-piece
Fo = focal length of the objective

v = L = length of the microscope tube,
and u = Fo

Hence,                  M = v/u (1+D/fe)

                                 = L/Fo(1+ D/fe)

The above relation shows that magnifying power is inversely proportional to the focal length of the objective and the focal length of the eye-piece. Therefore, magnifying power can be increased by
1. taking the objective of short focal length
2. taking the eye-piece of short focal length.


Practice Problems :
1. A simple magnifier (convex lens) has a focal length of 10 cm. Find its magnifying power.
Solution :
                  f = 10 cm
Magnifying power of a simple microscope(convex lens) M = 1+D/f 
              
⇒                M = 1+25/10     
                        = 1 + 2.5    
                        = 3.5                         { D = 25 cm for normal eye}

Magnifying power of simple convex lens of f = 10 cm is 3.5

2. A simple microscope is made of a combination of two lenses in contact of powers +15D and +5D. Calculate the magnifying power of the microscope, if the image is formed at 0.25m, the least distance of distinct vision.
Solution :   
               Powers of the two lenses are
                p1 = + 15 D
and           p2 = + 5D 
                D  = distance of distinct vision = 0.25 m
∴ Power of the combination, P = + 15 + (+5)
                                            = + 20 D 
∴ Focal length of the lens, f = 1/(+20)
                                        = 0.05 m
Now, magnifying power of simple microscope,

                                  M = (1+ D/f)
                                      = 1 + 0.25/0.05
                                      = 1 + 5 = 6 (Ans.)

Some practice problems :

1. An object is placed at a distance of 15 cm from a convex lens of focal length 30 cm. The size of image formed, in comparison to size of object is
(a) same                                   (b) double
(c) half                                      (d) 4 times

2. A simple magnifier(convex lens) has  a focal length of 10 cm. Its magnifying  power is :
(a) 0.1                                       (b) 2.5
(c) 3.5                                       (d) 10

3. Distance of distinct vision for a normal eye is :
(a) 5 cm                                     (b) 25 cm
(c) 50 cm                                   (d) infinity

4. In a simple microscope, the object is placed 
(a) between F and its lens            (b) at F
(c) between f and 2f                    (d) beyond 2f

5. Which of the following is not true ?
(a) Microscope is used to see small objects.
(b) Telescope  is used to see distant objects.
(c) In a microscope objective is larger than eye piece.
(d) In a telescope objective is larger than eye piece.

6. For a simple microscope if the final image is located at the least distinct vision D from the eye placed close to the lens, the magnifying power is :
(a) D/f                                   (b) 1 + D/f
(c) f/D                                   (d) f × D

7. Ratio of focal length of the objective to the focal length of the eye piece is greater than one for :
(a) telescope                                      (b) microscope
(c) both telescope and microscope       (d) neither telescope nor microscope

8. The final image produced by a simple microscope is :
(a) virtual and erect                           (b) virtual and inverted
(c) real and erect                               (d) real and inverted

9. A convex lens acts as a simple microscope when the object is placed
(a) between F and 2F                        (b) between optical centre and focus
(c) at 2F                                           (d) at F

10. The linear magnification of an image is m. The magnification for area will be
(a) m                                              (b) m/2
(c) m²                                                                  (d) m^1/2
  
11. As an object is moved from infinity towards the pole of a convex lens, the magnification of image will
(a) remain same                              (b) decrease 
(c) increase                                     (d) depend upon the presence of medium

12. Which of the following formula do not represent magnification by a lens– (where terms has usual meaning).
(a) I/O                                           (b) v/u
(c) (f – v)/f                                     (d) f/u

13. When the length of the tube of a compound microscope is increased, its magnifying power will
(a) increase                                  (b) decrease
(c) remain unchanged                    (d)become infinity

14. The magnifying power of a compound microscope in terms of magnification mo due to objective and magnifying power me by the eye piece is given by
(a) mo/me                                     (b) mo × me
(c) mo+me                                    (d) me/mo

15.If the least distance of distinct vision is 25 cm, then the convex lens of focal length 5 cm acts as a magnifier of magnifying power,
(a) 5                                          (b) less than 5
(c) 6                                          (d) more than 6

Optical Instruments

An optical instrument is an arrangement of lenses, prisms or mirrors, which enables us to see better than what we can see with the naked eye.

Optical Projection :
The process of obtaining distinct images on a screen or in a light sensitive device (the eye, photographic films etc.) of large distant objects, small nearly objects or fine details of large nearly object is known as  optical Projection. The devices used for getting the images in the above cases are called optical instruments.

The principle of optical instruments is to increase the angle of view for the image as compared to the viewing angle of the object. The angle of view is the angle at which rays from the extreme points of the object or its image converge at the optical centre of the eye.

Optical instruments provide a two dimensional (plane) image of a three dimensional object.

Types of Optical Instruments :
There are two types of optical instruments :
1. Optical instruments in which a real image is formed on the screen.
Examples : 
               Photographic camera, Magic lantern, Epidiascope, Cinema projector, Over head projector, Human eye etc. are the examples of this type of optical instruments.
2. Optical instruments in which a virtual image is formed and is directly seen with the eye.
Examples :
               Telescope, Microscope, Prism, Binoculars etc. are the examples of this type of optical instruments.