Electric Charges and Coulomb's Law MCQ Quiz - Objective Question with Answer for Electric Charges and Coulomb's Law - Download Free PDF

Calculation:
Let the charge on each sphere A and B be q and the separation be d.

Therefore, the force between spheres A and B is:

F = (1 / (4πɛ₀)) × (q² / d²) ... (1)

When spheres A and C are touched and then separated, charge on each will be:

(q + 0) / 2 = q / 2

Now sphere B is touched with sphere C. Charge on each will be:

(q + q/2) / 2 = (3q) / 4

Now the force between sphere A and sphere B will be:

F' = (1 / (4πɛ₀)) × (q/2 × 3q/4) / d²

= (3/8) × (1 / (4πɛ₀)) × (q² / d²)

⇒ F' = (3/8) × F

Calcultion:
The I-V characteristics shown in the figure represent a non-linear relationship between current (I) and voltage (V). This type of graph is typical of non-ohmic conductors, where the resistance varies with the applied voltage.

In contrast to ohmic conductors, where the I-V graph is a straight line (indicating constant resistance), non-ohmic conductors exhibit a curve, meaning their resistance changes with voltage.

Correct Answer: Option 2 - Non-ohmic conductors

Calculation:
The electrostatic force between two charges is given by Coulomb’s law:

F_e = (k × |q₁ × q₂|) / r²

Where:

• k is Coulomb’s constant (9 × 10⁹ N·m²/C²),
• q₁ and q₂ are the charges on the particles,
• r is the distance between the particles.

The gravitational force between two masses is given by Newton's law of gravitation:

F_g = (G × m₁ × m₂) / r²

Where:

• G is the gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²),
• m₁ and m₂ are the masses of the particles,
• r is the distance between the particles.

The forces cancel when:

F_e = F_g

Solving the equation, we find that the charge difference Δe (the difference between the proton and electron charge) is of the order of 10^-20 C.

Correct Answer: Option 4 - 10^-20 C

Calculation:

\(\phi=-2 \times 10^{4} \frac{\mathrm{Nm}^{2}}{\mathrm{C}}\)

r = 8.0 cm

\(\phi=\frac{\mathrm{q}}{\epsilon_{0}} \Rightarrow \mathrm{q}=\epsilon_{0} \phi \)

= (8.85 × 10^–12) × (–2 × 10⁴)

q = –17.7 × 10^–8 C

Ans.(4)

Sol.

The basic properties of electric charge are:

Charges are additive in nature.

Charge is a conserved quantity.

Quantization of charge.

CONCEPT:

Coulomb's law in Electrostatics –

• Coulomb's law state’s that force of interaction between two stationary point charges is directly proportional to the product of the charges, and inversely proportional to the square of the distance between them and acts along the straight line joining the two charges.

Force (F) ∝ q₁ × q₂

\(F \propto \;\frac{1}{{{r^2}}}\)

\(F = K\frac{{{q_1} \times {q_2}}}{{{r^2}}}\)

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

EXPLANATION:

Given – q₁ = 2 × 10^-7 C, q₂ = 3 × 10^-7 C and r = 30 cm = 30 × 10^-2 m

Force is equal to

\(F = \left( {9{\rm{\;}} \times {\rm{\;}}{{10}^9}} \right)\times \frac{{2 \times {{10}^{ - 7}} \times 3 \times {{10}^{ - 7}}}}{{{{\left( {30 \times {{10}^{ - 2}}} \right)}^2}}}\)

\( \Rightarrow F = \frac{{54 \times {{10}^{ - 5}}}}{{900 \times {{10}^{ - 4}}}} = 6 \times {10^{ - 3}}N\)

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 conductor is given by q = It, when current flows through the conductor for some time.

Where I = current and t = time

CALCULATION:

Given - I = 5 A and t = 2 min = 120 s

• The total charge on the conductor is given by q = It

⇒ Q = It

⇒ Q = 5 × 120 = 600 C

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.

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 conductor is given by q = It, when current flows through the conductor for some time.

Where I = current and t = time

EXPLANATION:

• 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.

Concept:

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

Concept:

• Charging: Charging means gaining or losing an electron. Matters can be charged with three ways, charging by friction, charging by contact, and charging by induction.
• Charging by friction: When you rub one material to another, they are charged by friction. Material losing electron is positively charged and material gaining electron is negatively charged. The amount of gained and the lost electron is equal to each other.

• Charging by contact: There are equal numbers of electrons and protons in a neutral matter. If something changes this balance we can say it is charged.
  • ‘A’ charged body (e. g; positively charged metal can) is brought in contact with uncharged body ‘B’. When in contact, negative charges from the uncharged body are attracted by the positive charges of the metal can. Finally, body B will remain with a net positive charge. Therefore, body B has been charged with positive charges.

• Charging by induction: A charged object is brought close to but does not touch the conductor. In the end, the conductor has charge of the opposite sign as the charge on the object. It is the process of charging by induction.

Explanation:

• During the process of charging by friction, the electrons are transferred from one material to another material.
• When an electron is transferred from for example glass to silk cloth, then the glass is positively charged and silk cloth is negatively charged respectively.
• The woolen cloth, inflated balloon and plastic scale can be charged easily by the friction method.
• But copper rod is a conductive material, so it can not be charged easily by charging by friction.

So, When we try to charge the copper rod by friction, it transfers the electrons because it is a good conductor.

CONCEPT:

• 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.

EXPLANATION:

• 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.

• People mistakenly think that an object gets a positive charge by receiving extra positive charges, it losses negative charge (electrons) to become positive.

Concept:

• Coulomb law: If two charges are placed at points separated by distance r force between charges is

1. Directly proportional to the product of charges.
2. Inversely proportional to the square of the distance

\(F=\frac{1}{4\piϵ_0}\frac{q_!q_2}{r^2}\)

• The dielectric constant is a ratio of the permittivity of material to the permittivity of vacuum.

\(K=\frac{ϵ}{ϵ_0}\)  Where,ϵ - permittivity of material and ϵ₀ - permittivity of vacuum. 

Explanation:

• In the first condition, charges are in the air

\(F=\frac{1}{4\piϵ_0}\frac{q_!q_2}{r^2} \) .................. (1)

• Then charges are placed in a material where force is 4F

​\(4F=\frac{1}{4\piϵ}\frac{q_!q_2}{r_1^2}\).....................(2)

• The dielectric constant(K) is 16 therefore permittivity of a material is given by
• ϵ = K ϵ₀ = 16 ϵ₀ 
• Substitute value of ϵ ​in equation 2

\(4F=\frac{1}{4\pi16ϵ_0}\frac{q_!q_2}{r_1^2}\) ..............(3)

• Divide equation 1 by equation 3

\(\frac{1}{4}= \frac{16r_1^2}{r^2}\)

​\(\frac{r_1^2}{r^2}=\frac{1}{64}\)

\(r_1=\frac{r}{8}\)

• Therefore option 1 is correct.

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. 

Additional Information

• Soap bubble exhibits the phenomenon of interference.
• When two light waves from different coherent sources meet together, then the distribution of energy due to one wave is disturbed by the other.
• The modification in the distribution of light energy due to the superposition of two light waves is called "Interference of light".
• The interference principle for light waves was promoted by T. Young.
• Optical interference shows the wave nature of light.

CONCEPT:

Electric Field Intensity:

• The electric field intensity at any point is the strength of the electric field at the point.
• It is defined as the force experienced by the unit positive charge placed at that point.

\(\vec E = \frac{{\vec F}}{{{q_o}}}\)

Where F = force and qo = small test charge

• The magnitude of the electric field is

\(E = \frac{{kq}}{{{r^2}}}= \frac{1}{{4\pi {\varepsilon _0}}}\frac{q}{{{r^2}}}\)

Where K = constant called electrostatic force constant, q = source charge and r = distance

CALCULATION:

Given distance r = 0.2 m, charge (q) = 1.6 × 10^-7 C

Electric field at a point 0.2 m from the center of the ball

\(E = \frac{1}{{4\pi {\varepsilon _0}}}\frac{q}{{{r^2}}}\)

Where ε₀ = the permittivity of free space.

\(\Rightarrow E = \frac{{9 \times {{10}^9} \times 1.6 \times {{10}^{ - 7}}}}{{{{\left( {0.2} \right)}^2}}} = \frac{{14.4 \times {{10}^2}}}{{0.04}} = 360 \times {10^2} = 3.6 \times {10^4}\;N/C\)

∴ The electric field at a point 0.2 m from the center of the iron ball = 3.6 × 10⁴ NC^-1

Mistake Points'r' here is the distance from the center of the iron ball, i.e. 0.2 m. It is not the radius of the ball.