Test: Electric Charge - JEE MCQ

This can be possible by induction, if a negative charge rod is placed near the sphere (at a distance not in touch) then it attracts positive charge inside the sphere towards its side and the negative charges collected on the other side and when the surface of the sphere connected to the earth than the negative charge goes to earth and the sphere remain positively charged.

Since rubbing the metal ball with fur and a piece of silk cloth involves touching, they can not be the correct answer. 

Therefore, the correct answer is C. 

From charge configuration, at the centre electric field is non-zero.

Potential at the centre due to 2q charge V_2q = 2q / r and potential due to -q charge

V_−q = −q / r (r = distance of centre point)

∴ total potential V = V_2q + V_-q + V_-q = 0

• Lightning is caused because of the build-up of electrostatic charges in the clouds.
• The electrical conductors are carriers of electric charges and can be dangerous when used while Lightning.
• A closed car nullifies the effect of lighting taking place outside. So, it is the best place to hide. But open cars are dangerous. 
• Usually, lightning does not affect short trees, and long trees are affected more. Though short trees provide good protection from lightning. 
• The electric pole is too dangerous during lightning. 

So, the correct option is Taking shelter in a car

Coulomb’s law: When two charged particles of charges q1 and q2 are separated by a distance r from each other then the electrostatic force between them is directly proportional to the multiplication of charges of two particles and inversely proportional to the square of the distance between them.

Force (F) ∝ q₁ × q₂

Where K is a constant = 9 × 109 Nm²/C²

Calculaton;
Given that:
q₁ = 2 C and q₂ = 2 C, r = 2 m
The force exerted by one charge q₁ on another charge q₂ is given by Coulomb's law:

So option (a) is correct.

Electric Charge

• It is defined as the intrinsic property of certain fundamental particles like electrons, proton, etc, due to which they produce electric and magnetic effects.
• Types of electric charge
  1. ​Positive charge: A body having a deficiency of electrons.
  2. ​Negative charge: A body having an excess of electrons.

Properties of electric charge

• Like charges repel and unlike charges attract each other.
• A charge is a scalar quantity.
• If a system contains a number of point charges, then the total charge of the system is obtained simply by adding all the charges algebraically.
• A charge is always quantized.
• A charge will always remain conserved.
• A charge is always associated with mass.
• The unit of charge is the coulomb.

Avogadro number: One mole of a substance is equal to 6.022 × 10²³ units of that substance (such as atoms, molecules, or ions).

• The number 6.022 × 10²³ is known as Avogadro's number or Avogadro's constant.
• The concept of the mole can be used to convert between mass and number of particles.
• The charge on the 1 mole of the electron is 1.6 × 10-19 C and the mass of an electron is 9.1 × 10-31 kg.

So,

• ​Positive charge: A body having a deficiency of electrons.
• Negative charge: A body having an excess of electrons.

We know that the charge on the electron is 1.6 × 10-19C, and the mass of the electron is 9.1 × 10-31Kg.

And the specific charge of any particle is the charge per kilogram of the particle.

Hence to find the specific charge we divide the charge of one electron by the mass of a single electron. 

∴ Specific charge = (1.6 x 10-19 ) / (9.1 x 10^-31) = 1.8 x 1011 C/kg

Millikan's Oil drop experiment: 

• In this experiment, Milliken allowed charged tiny oil droplets to pass through a hole into an electric field.
• By varying the strength of the electric field the charge over an oil droplet was calculated, which always came as an integral value of charge on one electron.

Davisson-Gomer's experiment:

• Initially, the atomic models proposed by various scientists could only explain the particle nature of electrons but failed to explain their wave nature.
• In the year 1927 C.J. Davisson and L.H. Germer perform an experiment, which is known as Davisson Germer’s experiment by which they explain the wave nature of electrons through electron diffraction.

Compton scattering experiment:

• Compton effect is defined as the effect that is observed when x-rays or gamma rays are scattered on a material with an increase in wavelength.
• Arthur Compton studied this effect in the year 1922.
• During the study, Compton found that wavelength is not dependent on the intensity of incident radiation.
• It is dependent on the angle of scattering and on the wavelength of the incident beam.

Raman effect: Raman effect is defined as the scattering of photons by the excited molecules that are at higher energy levels.

• When a negatively charged body is grounded electrons from the body flow to the earth and the body becomes neutral.
• On the other hand, when a positively charged body is grounded electrons coming from the earth neutralize the body.

Additional Information: Earth is an electric conductor. Earthing is defined as “the process in which the instantaneous discharge of the electrical energy takes place by transferring charges directly to the earth through low resistance wire.” When a charged body is connected to the earth, it becomes electrically neutral. 

• Electric charge: It is an intrinsic property of the elementary particles of matter which gives rise to electric force between various objects.
• It is a scalar quantity.
• SI unit of electric charge is coulomb (C).
• The total charge on the conductor is given by q = It, when current flows through the conductor for some time.

Where I = current and t = time

Solution:

• When a soap bubble is charged, then the charged particle will uniformly be distributed over the surface of the soap bubble.
• Hence the radius of the soap bubble will increase because the charged particles are uniformly distributed on the soap bubble and this will cause them to repel each other due to the electrostatic force. Therefore option 2 is correct.

Electric charge(q): The property of matter which is responsible for electrostatic force is called an electric charge.

The SI unit of charge is coulomb (C).

The rate of flow of electric charge is called an electric current.

Charge (q) = current (I) × time (t)

Calculation:

Given that;

Current (I) = 0.5 A

Time (t) = 20 min = 20 × 60 sec = 1200 sec

Amount of electric Charge (q) = current (I) × time (t) = 0.5 × 1200 = 600 C

Charge: The property of matter that is responsible for electrical phenomena is called charge. The charge is of two- types positive and negative.

Law of charge conservation: Charge is neither created nor destroyed; it can only be transferred from one system to another.

• The total charge on the two spheres will be conserved by the law of charge conservation
• But energy may not conserve because if they are of a different size or have different charge then some of their energy might lose in the redistribution of charge.
• In the case of the final potential, it is not always the mean of original potential because during the redistribution of charge some losses occur, but final potential on both spheres is always equal.
• Charge: The property of matter that is responsible for electrical phenomena is called charge. The charge is of two- types positive and negative.
• Law of charge conservation: Charge is neither created nor destroyed; it can only be transferred from one system to another. 

• The total charge on the two spheres will be conserved by the law of charge conservation
• But energy may not conserve because if they are of a different size or have different charge then some of their energy might lose in the redistribution of charge.
• In the case of the final potential, it is not always the mean of original potential because during the redistribution of charge some losses occur, but final potential on both spheres is always equal.

The correct answer is its radius increases.

• What happens when some charge is placed on a soap bubble its radius increases.

Key Points

• The radius of the bubble will expand because the charged particles uniformly distributed on it causes them to repel each other due to the electrostatic force.
• The phenomenon takes place in both positive and negatively charged bubbles because of the charge on it. 

• He atom has 2 electrons.
• So, 1 mole of He has 2*N(N is Avogadro's no.) electrons.
• Then total -ve charge in 1 mole He gas is =  2 * N * charge of 1 electron
  = 2 * (6.022 * 10²³) * (1.6 * 10^-19) = 1.92 * 10⁵ C 

Electric Charge

• It is defined as the intrinsic property of certain fundamental particles like electrons, proton, etc, due to which they produce electric and magnetic effects.
• Types of electric charge
  1. ​Positive charge: A body having a deficiency of electrons.
  2. ​Negative charge: A body having an excess of electrons.
• Properties of electric charge
  • Like charges repel and unlike charges attract each other.
  • A charge is a scalar quantity.
  • A charge is always quantized.
  • A charge will always remain conserved.
  • A charge is always associated with mass.
  • The unit of charge is the coulomb.

⇒ 1 coulomb = charge on 625 × 1016 electrons

• ​Positive charge: A body having a deficiency of electrons and the number of protons becomes more than the number of electrons.
• ​Negative charge: A body having an excess of electrons and the number of electrons becomes more than the number of protons.
• Neutron is not responsible for the charge on the element.
• The number of neutrons becomes more than the number of electrons in the element, by this statement, we can't predict whether the number of protons is more than, less than, or equal to the number of electrons in the element.
• So we can't predict the type of charge on the element. Hence, option D is correct.

Concept:

• Electric charge: It is an intrinsic property of the elementary particles of matter which gives rise to electric force between various objects.
• It is a scalar quantity.
• SI unit of electric charge is coulomb (C).

So,

• Like charged repel each other. Therefore option B is incorrect statement and hence correct answer.

The correct answer is option 1) i.e. 2μC.
Electric charge is a property of particles by which they have a tendency to attract or repel each other without touching. 

• Electric force: Particles possessing opposite charges attract each other and particles possessing like charges repel each other. This force of attraction or repulsion is called electric force.

Coulomb's law: The relationship between the electric charges and electric force is given by Coulomb's law.

• Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the distance between the two objects.

The electric force is given as:

​Where F is the electric force acting between the two charges, q₁ and q₂ are the two charges, r is the center to center distance between the two objects and k is the proportionality constant known as the Coulomb's law constant and is equal to 9 ×10⁹ Nm²/C².

Given that:
The two charges q₁ and q₂ are identical ⇒ q₁ = q₂ = q
Electric force (F) of repulsion between the charges = 10 g wt = 10 ×10^-3 kg ×10 m/s² = 0.1 N
Distance between the two charges (r) = 0.6 m

Therefore, the identical charges are 2μC.

Electric Charge

• It is defined as the intrinsic property of certain fundamental particles like electrons, proton, etc, due to which they produce electric and magnetic effects.
• Types of electric charge
  1. ​Positive charge: A body having a deficiency of electrons.
  2. ​Negative charge: A body having an excess of electrons.
• Properties of electric charge
  • Like charges repel and unlike charges attract each other.
  • A charge is a scalar quantity.
  • A charge is always quantized.
  • A charge will always remain conserved.
  • A charge is always associated with mass.
  • The unit of charge is the coulomb.

⇒ 1 coulomb= charge on 625×1016 electrons

So,

• ​Positive charge: A body having a deficiency of electrons.
• We know that the proton is present in the nucleus so we can't add or remove protons in the element but we can add or remove electrons from the element.
• So the body can be positively charged by removing electrons and negatively charged by adding electrons.
• A charge cannot be generated by adding or removing protons. Hence, option 2 is correct.

During rubbing, glass rod acquires + ve charges and silk cloth acquires - ve charges.
The glass rod will have postive charge equal in value to the negative charge lost by the silk.
∴ the charge on the glass rod is + 1.6×10^{- 19}C

Additional Information: When a glass rod is rubbed with silk, glass happens to lose electrons easily and silk grabs them away from the glass atoms. So after rubbing, the glass becomes positively charged and the silk becomes negatively charged. Thus equal but opposite charges are produced on both. 

Concept:

• Electric charge: It is an intrinsic property of the elementary particles of matter which gives rise to electric force between various objects.
• It is a scalar quantity.
• SI unit of electric charge is coulomb (C).
• The total charge on the body is always an integral multiple of a basic quantum of charge i.e. q = ne

Where n = integer
If a system has n charges like q₁,q₂,q₃,...q_n.

• Then their total charge will be sum of all charges i.e.
  ⇒ (q₁ + q₂ + q₃ + …q_n)
• This is called a principle of superposition of charges. Therefore statement 1 correct. 
• It is the property of charges that is, like charges repel each other whereas unlike charges attract each other. Therefore statement 2 is incorrect and statement C is correct.

Coulomb's Law: The force between two charges is given by:

• where:

  • k is Coulomb's constant,
  • q₁​ and q_2​ are the charges,
  • r is the distance between the charges.

• Forces on −2q:

  • The charge −2q experiences two forces:
    1. Force F₁​ due to the leftmost charge +q:

• Since the charge −2q is negative, it is attracted to the leftmost charge +q, so the force F_1​ points to the left.
  2. Force F₂​ due to the rightmost charge +q: 
  The force F_2​ also attracts the negative charge −2q, so F₂​ points to the right.
  3. Net Force: The two forces F_1​ and F_2​ are equal in magnitude but act in opposite directions. Therefore, they cancel each other out:

• F_net = F₁ −F₂ = 0

If an object is positively charged it loses some of its electrons. The mass of an electron is 9.11 x 10^-31 kg. So, if a positively charged body loses ‘n’ number of electrons, it mass decrease by the amount n x 9.11E^-31kg.