LECTURE 3 : CLASS XII: PHYSICS : ELECTRIC FIELD

CLASS XII   |    PHYSICS    |    CHAPTER 1

      notes prepared by subhankar Karmakar

(the physical quantity written in bold letters are vectors )

ELECTRIC FIELD: 

The electric field or electric intensity or the electric field strength E at a point is defined as the force experienced by a unit positive test charge placed at that point, without disturbing the position of source charge. 

• Electric field E is a vector quantity. 

• SI unit of electric field is N/C. 

• Dimension of electric field is

 [E] = force/charge = [MLT⁻²]/[AT] = [MLT⁻³A⁻¹]

Electric field is an example of vector field:

As the value of electric field E is different at different point, so we can say each point having a position vector r , therefore, the vector E is a function of position vector of a point. Hence, we can say electric field is an example of vector field. 

Principle of superposition of electric fields:

It says the electric field at any point due to a group of charges is equal to the the vector sum of the electric field produced by the each charge individually at that point, when all other charges are assume to be absent. 

LECTURE 1 : CLASS XII: PHYSICS : ALTERNATING CURRENT (AC)

CLASS XII   |    PHYSICS    |    CHAPTER 1

      notes prepared by subhankar Karmakar

Alternating current:

An alternating current is that current whose magnitude changes continuously with time and direction reverses periodically. 

When a coil is rotated in a magnetic field, an alternating EMF is induced in it which is given by the relation

ℰ = ℰₒ sin (ⲱt) ---------------------------- (i)

When applied to a circuit of resistance R, it will produce a current Ｉ such that

Ｉ = ℰ/R = (ℰₒ/R) sin (ⲱt) = Ｉₒ sin (ⲱt)--------(ii)

Therefore, the current in the circuit varies sinusoidally with time and it is called alternating current. 

Ｉ = Instantaneous Current

Ｉₒ = ℰₒ/R = Maximum or peak value of current. It is also called current amplitude. 

Amplitude: The maximum value attained by an alternating current in either direction is called its amplitude or peak value and is denoted by Ｉₒ. 

Time Period: The time taken by an alternating current to complete one cycle of its variations is called its time period and is denoted by T.

This time is equal to the time taken by the coil to complete one rotation in the magnetic field. 

T = 2π/ⲱ ; where ⲱ = angular velocity of the coil. 

Frequency: The number of cycles completed per second by an alternating current is called its frequency and is denoted by f. It is equal to the frequency of rotation of the coil in the magnetic field. 

f = 1/T = ⲱ/(2π)

∴ Ｉ = Ｉₒ sin (ⲱt) = Ｉₒ sin (2πft) = Ｉₒ sin (2πt/T) -------- (iii)

• In India AC supply has a frequency of 50 Hz

Mean / Average Value of AC over a half cycle:

Average value of AC : It is defined as that value of direct current which sends the same charge in a circuit in the same time as is sent by the given alternating current in its half time period. It is denoted by Ｉₘ or Ｉₐᵥ.

LECTURE 2 : CLASS XII: PHYSICS : ELECTRIC CHARGE & FIELD NUMERICALS

CLASS XII   |    PHYSICS    |    CHAPTER 1

      notes prepared by subhankar Karmakar

Numericals on quantization of charge:

1. Which is bigger 1 coulomb or a charge on an electron? How many electronic charges form one coulomb of charge?

2. If a body gives out 10⁹ electrons every second, how much time is required to get a total charge of 1 coulomb from it?

3. How much positive and negative charge is there in a cup of water? (Take the mass of water contained in a cup is 250 g).

4. Calculate the charge carried by 12.5 x 10⁸ electrons. 

5. Estimate the total number of electrons present in hundred gram of water. How much is the total negative charge carried by these electrons? (Take Avogadro number = 6.02 x 10²³ and molecular mass of water = 18).

Numericals on Coulomb's law of electrostatics:

6. Two particles, each having a mass of 5 gram and charge 0.1 microcoulomb , stay in limiting equilibrium on a horizontal table with a separation of 10 centimetre between them. The coefficient of friction between each particle and the table is same. Find the coefficient of friction.

7. Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 x 10⁻⁷ C ? The radii of A and B are negligible compared to the distance of separation. What will be the force of repulsion if the two spheres are placed in water?

8. Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally remove from both. What is the new force of repulsion between A and B?

9. Two similarly equally charged identical metal spheres A and B repel each other with a force of 2.0 x 10⁻⁵ N. A third identical unchaged sphere C is touched to A, then placed at the mid point between A and B. Calculate the net electrostatic force on C. 

10. Two identical charges, Q each, are kept at a distance r from each other. A third charge q is placed on the line joining the above two charges such that all the three charges are in equilibrium. What is the magnitude, sign and position of the charge q?

Numericals on the superposition principle:

11. Consider three charges q₁, q₂, q₃ each equal to q at the verices of an equilateral triangle of side l. What is the force on a charge Q placed at the centroid of the triangle?

12. Consider the charges +q, +q and -q placed at the vertices of an equilateral triangle. What is the force on a charge?

13. Four equal point charges each 16 μC are placed on the four corners of a square of side 0.2 m. Calculate the force on any one of the charges. 

1 mark questions:

1. Two identical metallic spheres of exactly equal masses are taken. One is given a positive charge q and other an equal negative charge. Are their masses after charging equal?

2. Can two like charges attract each other? If yes, how?

3. Electrostatic experiments do not work well on humid days.  give reasons. 

4. A comb runs through one's dry hair attract small bits of paper. Why? What happens if the hair is wet or if it is a rainy day?

5. Ordinary rubber is an insulator. But the special rubber tyres of aircrafts are made slightly conducting. Why is this necessary?

6. Vehicles carrying inflammable materials is usually have metallic ropes touching the ground during motion. Why?

7. An inflated balloon is charged by rubbing with fur. Will it stick readily to a conducting wall or to an insulating wall? Give reason.

8. What does q₁ + q₂ = 0 signify in electrostatics?

9. Can a body have a charge of 2.4 x 10⁻¹⁹ C? Justify your answer by comment?

10. If the distance between two equal point charges is doubled and their individual charges are also doubled, what would happen to the force between them?