Static Electricity

Chapter- 10

Question/Answer:

1. What is charge?

Ans: The basic and characteristical property of the fundamental particles of material is the charge.

Everything is made of an atom and molecule. There are 118 atoms in this world, among which 83 are stable, only with these atoms millions of different molecules are formed.

Atom is the building block of everything. The nucleus is the center of an atom and electrons revolve around the nucleus. The nucleus consists of a proton and a neutron. A proton is positively charged while a neutron is chargeless and an electron is negatively charged.

The charge of a proton and electron is equal but opposite and

the magnitude of this charge is 1.6 x 10-¹⁹ coulomb.

In an atom generally, there are the same number of electrons and protons

and so an atom is charge neutral.

Hydrogen is the simplest atom. The nucleus of hydrogen atom consists of only one proton

and only one electron is revolving around it.

2. What is electrical energy?

Ans: If there is a potential difference between two terminals of a conductor,

then there is a flow of electrons.

Electric potential:

The amount of work done for bringing a positive unit charge from infinity to a point in an electric field is known as the electric potential of that point.

The point where electric field intensity is zero is the neutral point.

The process of making an uncharged object charged only by the presence of a charged object, not by touching it, it is known as electrical induction.

The potential of a positively charged conductor is known as positive potential.

The intensity of the electric field is the electric field intensity.

The potential of a positively charged conductor is known as positive potential.

Equipment that is used to determine the existence and nature of charge in an object, is known as electroscope.

Electric force is the force at which the charged particles attract or repel each other.

Electric induction: The process of making an unchanged object charged only by the presence of a charged object.

Q. Describe the conduction of a gold-leaf electroscope.

Ans: The structure of a gold leaf electroscope:

For the detection and testing of small electric charges, a gold-leaf electroscope is used. This instrument was invented towards the end of the eighteenth century by a Yorkshire clergyman named Abraham Bennet. The figure shows a common type of electroscope.

An electroscope is a wonderful equipment for the test of static electricity. The equipment is very simple to determine the presence of a charge, it contains two light leaves of gold, aluminum, or some other metal. These two leaves are connected to a metal disc by a highly conducting rod. The whole setup is kept inside a glass bottle with a nonconducting stopper so that it can be seen from outside, but air or anything else cannot touch the light metal leaves.

If a glass rod is rubbed with silk, a positive charge is accumulated in the rod. Now if the glass rod touches the metal disc of the electroscope, some charge will immediately go to the disc. As the disc is connected with the metal rod and the leaves, the charge will spread everywhere. When similar charges appear in the gold leaves, the leaves will repulse each other and create a gap between them.

Q. Describe how a gold-leaf electroscope can be charged positively.

Ans: The process of charging a gold-leaf electroscope positively:

Let us earth the cap of an electroscope by touching it momentarily with a finger, making it zero potential (fig. a), and place a positively charged rod near the cap of the electroscope (fig. b); equal and opposite amounts of charge in the cap/stem system separate out leaving the system at a positive potential (+V).

Keeping the positively charged rod in place, let us again earth the cap of the electroscope with a finger and note that the leaf falls.

The potential of the cap/stem V is now zero (fig. c), even though the cap of the electroscope carries a negative charge and the stem a positive charge.

Coulomb's Law:

The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them and this force acts along the line joining the two charges.

If mass m1 and m2 are replaced by q₁ and q₂, we get Coulomb's law. G was the constant for gravitational force, now we will use the constant k. This is the difference. That is, if two charges, q₁ and q₂ are placed at a distance r, the force working between them will be,

F = k q₁q₂/ r²

Here the unit of the two charges q₁ and q₂ is C and of distance is m, so we may say, the unit of k will be Nm²/C², so that the unit of F becomes N.

The value of k:

k = 9 x 10⁹ Nm²/ C²

Coulomb is the unit of charge. Coulomb is to understand the amount of charge of an electron or proton. Its amount is:

Charge of electron: - 1.6 x 10-¹⁹ C

Charge of proton: + 1.6 x 10-¹⁹ C

If q₁ and q₂ both are positive or negative, then the value of F is positive and they will repel one another. If one charge is positive and the other is negative, then the value of F will be negative, which means the direction of the force is charged, that is, the charges will attract one another.

Q.1. A +1 C charge and a - 1 C charge are placed at a distance of 10 cm.

How much force is acting between them?

Ans: Two opposite charges will attract each other. The force acting between them

We know,

F = k q₁q₂/ r²

Given here,

q₁ = 1 C

q₂ = - 1 C

r = 10 cm = 0.10 m

k = 9 x 10⁹ Nm²/C²

So, F = 9 x 10⁹ x 1 x (-1) / (0.10)² N

= - 9 x 10¹¹ N

Q. 2. Two charge of +5 C and +3 C are placed at a distance of 1m. Now a third charge +q is placed in between them, where will it not feel any force.

Ans: The +5 C charge will repel + q charge towards the right and the +3 C charge repel towards the left. When two charges will repel by equal force, +q change will not feel any force.

So, K )+5)q / x² = K (+3) q / (1 - x)²

5( 1 - x) ² = 3x²

2x² - 10x + 5 = 0

x = 4.435

As the value of x will be between 0 and 1, so the value of x must be 0.565.

Q.3. There is a proton in the center of a hydrogen atom and an electron outside it. The charges of the proton and electron are +1.6 x 10-¹⁹ C and - 1.6 x 10-¹⁹ C respectively. If the distance of the orbit of the electron from the nucleus is 0.5 x 10 -⁸ m, how much attraction is found between them?

Ans: We know,

F = k q₁q₂/ r²

Given here,

q₁ = +1.6 x 10-¹⁹ C

q₂ = - 1.6 x 10-¹⁹ C

r = 0.5 x 10 -⁸ m

k = 9 x 10⁹ Nm²/C²

therefore, F = - 9.22 x 10 -¹² N

Q.4. How much charge should be stored in the earth and the moon so that the gravitational force becomes zero and the moon goes out of its orbit?

Ans: The gravitational force acting between the earth and the moon

F🇬 = G mM/r²

Given here, G = 6.67 x 10-¹¹ Nkg-²m²

m = 7.35 x 10²² kg

M = 5.97 x 10²⁴

r = 3.84 x 10⁶ km

So,

F🇬 = G mM/r²

= 1.98 x 10²᠐ N

If an equal amount of charge is kept in the earth and moon, the repulsive force.

Electric field cannot be seen, but to make it easy to understand, sometimes one type are drawn, called the electric lines of force.

Q.5. What is the magnitude of the electric field at a distance of 10m for 5 C charge?

Ans: We know,

E = K q/r²

Given here, q = 5 C

q2 = - 1.6 x 10 -¹⁹

r = 10 m

k = 9 x 10⁹ Nm² /C

So,

E = 4.5 x 10⁸ N/C

Q.6. A charge of 3 C is experiencing a force of 10N.
What is the electric field?

Ans: We know ,

F = qE

So, E = F/q

Here, F = 10N

q = 3C

Therefore, E = F/q

= 10N/3C

= 3.33 N/C

Electric Potential:

The amount of work done for bringing a positive unit charge from

infinity to a point in electric potential of that point.

If r is the radius of a metallic sphere and if it is given charge Q

then its potential will be V

V = Q/C

Here C is the capacitance of the sphere.

The value of C for a metallic sphere is

C = r/k

Where, k = 9 x 10⁹ Nm²/C²

So, if there are two metallic spheres of radius R1 and R2

and both are given the same amount of charge Q,

the sphere having the lower radius will have the higher potential.

If the two spheres are connected using a wire,

then change will flow from the smaller sphere to the bigger sphere

until the potential of the two spheres becomes the same.

For example, let's assume positive Q charge is given to a metallic

sphere of radius r, and then the potential of its surface is

v = kQ/r

You know due to the presence of charge in a sphere,

electric field E is created around it. So if a charge q is brought to it,

the charge will experience a force F where,

F = Eq

If W is the amount of work done to bring the charge q then potential V is,

V = W/q

A capacitor is a device that stores electrical energy in an electric field. When heat is applied to a body, the amount by which its temperature rises depends on the heat capacity of that body. When the value of heat capacity is large enough, the temperature rise will be small even if a huge amount of heat is given to that body.

When the capacitance of a body is C and if Q amount of charge is

given to the body, then the potential V will be

V = Q/C

We have seen already that for a metallic sphere of radius r, the capacitance C is:

C = r/k

But the most simple and effective capacitor is made by keeping two metal plates side by side. If one plate is charged positively and the other is charged negatively, then an electric field is developed between the plates and energy is stored in that electric field. For a capacitor, if capacitance is C and voltage is V, then the energy stored in it is: