Test: Coulomb's Law

Concept:
According to Coulomb's law, the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between their centres.

where, 
F = Electrostatic force
q₁ and q₂ are point charges
r = distance between two point charge
 = Proportionality constant
where, 
ε₀ = Absolute permittivity of vacuum or air
ε_r = Relative permittivity of the medium in which charges are placed. For vacuum or air, its value is 1
The value of ε0 = 8.854 × 10^-12 F/m
Calculation:
Given,
q₁ = q₂ = 3 x 10^-7 C
F = 0.5N
∵ The medium is vacuum so ε_r = 1

⇒ r = 0.04 m

It states that the 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.

F ∝ q₁ ∝ q₂    

Where 

also called Coulomb's constant or electrostatic force constant.
Here ϵ₀ = Permittivity of free space.
The value of K depends on the nature of medium between the two charges and the system of units chosen.

CONCEPT:
Superposition Principle: 

• The principle of superposition states that when a number of charges are interacting, the total force on a given charge is the vector sum of the forces exerted on it due to all other charges.
• The force between two charges is not affected by the presence of other charges.
• This is used to calculate the following parameter at the observation point, to any configuration of charges.
  • Net force.
  • Net electric field.
    

Coulomb's law in Electrostatics:

• It 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.
  
  F ∝ q₁ × q₂  
  

Where K = constant called electrostatic force constant.

• The value of K depends on the nature of the medium between the two charges and the system of units chosen

CONCEPT:
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 
Calculations:
Consider new charge + 4μC is placed d m apart from old +4 μC charge and (x + 0.6) m apart from -16 μC charge.

Let,
q_A = + 4 μC at point A
q_B = - 16 μC at point B
q_C = + 6 μC at point C

Since, net force on charge q_C will zero.
∴ |F_CA| = |F_CB|
From above concept,

4d² = (0.6 + d)²
4d² = 0.36 + d² + 1.2d
3d² - 1.2d - 0.36 = 0
d₁ = - 0.2 m
d₂ = + 0.6 m
Hence, according to option + 0.6 m distance should a third charge of + 6 μC be placed from + 4 μC so that no force exerts on it will be zero.

Coulomb’s Law: It states that the force between two charged particles will be directly proportional to the product of the quantity of the two charges.
F ∝ Q₁Q₂,
Secondly, it is also inversely proportional to the square of the distance between them, i.e.
F ∝ 1/r2 
∴ The force between two charges Q₁ and Q₂ is given by:

where k is the proportionality constant and is equal to 9 × 10⁹ Nm²/C².

Concept:

• Coulomb’s law: When two charge 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 multiplication of charges of two particles and inversely proportional to square of distance between them.

Force (F) ∝ q₁ × q₂    

Where K is a constant = 9 × 10⁹ Nm²/C² 
Case 1:
Given that charges are: Q₁ and Q₀₀
Distance = d
Force (F₁) = 20 mN

Case 2:
The charges of both particles are doubled and distance between them is also doubled.
Given that charges are: 2Q₁ and 2Q₂
Distance = 2d

Therefore, the force remains same and it is equal to 20 mN

CONCEPT:
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  

• Coulomb’s Law talks about the magnitude of the attraction between the two charges.
• It says that the force is directly proportional to the product of the quantity of the two charges and inversely proportional to the square of the distance between them. 

Lenz’s Law:

• It states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.
• When a current is induced by a magnetic field, then the magnetic field produced by the induced current will create its magnetic field.
• Thus, this magnetic field will be opposed by the magnetic field that created it.

Concept:
The force acting on a point charge because of another point charge is given as:
 (Where â_r is a unit vector in the direction of the force)
Calculation:
Given Q₁ = 4π × 10^-3 C
Q₂ = 8.854 × 10^-9 C

Since, we are asked to find the force on Q₂ due to Q₁, the direction of the force 
= â_r   

So, the Force on Q₂ due to Q₁ will be:

= a_y N

CONCEPT:
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  

• Coulomb’s Law talks about the magnitude of the attraction between the two charges.
• It says that the force is directly proportional to the product of the quantity of the two charges and inversely proportional to the square of the distance between them.