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Electrostatic Forces - Part One
The four fundamental forces of nature
Weak force
Strong force
Gravitational force
Electromagnetic force
Useful information:
Any atom consists of
a nucleus containing positively charged protons and neutral neutrons
and negatively charged electrons orbiting around it in elliptical orbits
The atom is electrically neutral?
Number of protons = Number of electrons
Charge of proton = Charge of electron
𝑞𝑒 = 𝑞𝑝 = 1.602 X 10-19c
Electrons are what are gained or lost
Charged bodies contain protons and electrons but their numbers may be different
A negatively charged body has gained electrons
(Number of electrons > Number of protons
)
A positively charged body has lost electrons
(Number of protons > Number of electrons
)
The charge of a body can be expressed by knowing the number of protons and electrons in the body
using the following relation
Evaluate yourself
A charged body has 32 more protons than electrons. The charge of the body is
equivalent to
Click here to show solution
Choose the correct answer
Evaluate yourself
A neutral body gained 8 electrons. The charge of the body is equivalent to
Click here to show solution
Choose the correct answer
: Charges are conserved in a closed system
When rubbing a piece of wool with an ebonite rod,
the wool loses electrons and becomes positively charged and
the ebonite rod gains electrons and becomes negatively charged
Number of electrons lost by the wool = Number of electrons gained by the ebonite rod
(In a closed system)
Evaluate yourself
A balloon was rubbed with a piece of wool and became negatively charged with a charge of
8 X 10-19c
Then the piece of wool has lost
Click here to show solution
Choose the correct answer
: Quantized Charge
Millikan was able to prove that a charged oil droplet is charged with integer multiples of the charge of a single electron.
Using the Millikan oil-drop apparatus, the scientist was able to calculate the charge of the oil droplet.
When dividing the charge by the elementary charge, the result was an integer, confirming that charge is quantized.
Millikan Oil Drop Experiment Simulation
Millikan Oil Drop Experiment
Formulas Used:
1. Electric field
\[ (E) =\frac {V}{d}\]
2. Volume of spherical oil drop
\[ V = \frac {4}{3}πr³\]
3. Mass (m) = Density (ρ) × Volume (V)
4. Charge
\[(q) = \frac {(m × g × d)}{ V}\]
5. Number of electrons
\[(n) = \frac {q }{ e}\]
(where e = 1.6 × 10⁻¹⁹ coulombs)
When examining protons and neutrons, it was found that they contain quarks with very small masses bound together by gluons.
Down quarks with negative charge
Up quarks with positive charge
\[-\frac{1}{3}e\]
\[+\frac{2}{3}e\]
.............................. : Solution
A proton contains two up quarks and one down quark - determine the proton's charge
.............................. : Solution
A neutron contains one up quark and two down quarks - determine the neutron's charge
Solved Example
An iron block with mass of 1.4 kg
\[1.4 \; Kg\] and a negative charge of 0.4 c
\[0.4\;c\] - what is the ratio of electrons gained?
Given that the molar mass of iron
\[56\;g\] and its atomic number is 26
Solution Method:
Every 1 mole of any substance contains Avogadro's number of atoms
6.022 X 1023 atoms
One mole of iron has a mass of 56 grams
First calculate the number of atoms in 1.4 kg mass
\[N=\frac{6.022×10^{23}×1.4×10^3}{56}= 1.5055 × 10^{25}\]
The atomic number is the number of protons in the atom (number of protons = number of electrons) for iron atom = 26
Number of electrons in 1.4 kg mass
\[N= 26 ×1.5055 × 10^{25}= 3.9143 × 10^{26}\]
The ratio of gained electrons is the number of gained electrons to the total number of electrons
To calculate the number of gained electrons
\[n=\frac{0.4}{1.6× 10^{-19}}= 2.5× 10^{18}\]
To calculate the ratio of gained electrons
\[\frac{2.5× 10^{18}}{3.9143 × 10^{26}}=6.38 × 10^{-9}\]
Conductors, Insulators, Semiconductors and Superconductors
Conductors:
Materials that can conduct electric current because they contain free electrons capable of moving through the material like copper, iron, and aluminum.
Insulators:
Materials that cannot conduct electric current because their electrons are bound to the nucleus and cannot move through the material like wood, plastic, and ebonite.
Semiconductors: Materials that can conduct current under special conditions like germanium and silicon (Group 14 elements).
These materials contain four valence electrons that form covalent bonds between atoms at absolute zero temperature (-273°C).
At absolute zero, they cannot conduct, but at room temperature some bonds break and they become conductive.
When doping semiconductors with impurities from Group 15 elements (N-type donors).
Doping is done with one impurity atom per million host atoms, making electrons the charge carriers.
When doping semiconductors with impurities from Group 13 elements (P-type acceptors).
Doping is done with one impurity atom per million host atoms, making holes the charge carriers.
Superconductors:
Materials with almost zero resistance to current flow, which only work at very low temperatures like titanium.
Types of Electric Charging
Types of Electric Charging
Charging by Friction
Scientific Explanation:
This phenomenon occurs when two different objects are rubbed together, causing electrons to transfer from one object to another due to differences in materials' electron affinity.
Electromagnetic Interaction:
- Material with higher electron affinity (like wool) loses electrons
- Material with lower electron affinity (like plastic) gains electrons
Practical Applications:
- Van de Graaff generators
- Electrostatic painting systems
- Air purification systems
- Educational experiments about static electricity
Primary Purpose:
Generating static electric charges by transferring electrons between materials, maintaining the acquired charge for relatively long periods.
Charging by Induction
Charging by Induction
Definition:
A process of separating electric charges in a conductor without direct contact with the charged object, where charges in the neutral body are affected by the electric field of the charged object.
Process Steps:
Bring a charged object (like a negatively charged rod) near a neutral conductor
Polarization occurs in the neutral body (positive charges approach, negative charges move away)
Ground the conductor
Remove the ground connection then remove the charged object
The conductor becomes charged with opposite charge to the inducing object
Practical Example:
When bringing a negatively charged balloon near an aluminum can:
Positive charges in the can are attracted toward the balloon
Negative charges move to the far side
If the can is grounded, negative charges transfer to earth
After removing the balloon, the can remains positively charged
Key Characteristics:
- No direct contact between objects needed
- Resulting charge is opposite to the inducing charge
- Causes temporary charge redistribution
- Based on the law of conservation of charge
Comparison Between Conductors and Insulators
Comparison Between Charging Conductors and Insulators
Property
Conductors
Insulators
Electron Movement
Free-moving electrons
Bound electrons
Electrical Conduction
✅ Excellent conduction
❌ No conduction
Thermal Conduction
✅ Good heat conduction
❌ Poor heat conduction
Examples
Copper, silver, aluminum
Wood, glass, rubber
Surface Charging
Charges spread on surface
Charges remain localized
Applications
Electrical wiring
Wire insulation
Scientific Explanation:
Conductors: Contain free electrons in their outer atomic orbitals, allowing easy movement of electric charges through the material.
Insulators: Have electrons tightly bound to their nuclei, preventing free movement and thus blocking electric current flow.
Charge Conservation Law:
When charging a conductor:
- Charges move to the outer surface
- Charges distribute evenly
Environmental Impact:
Insulators play crucial roles in:
- Preventing electric shocks
- Maintaining current stability
- Reducing energy loss
When bringing a charged object near a conductor, charge redistribution occurs, while in insulators the positive and negative charge centers separate without movement
Charging an Electroscope by Induction
Charging an Electroscope by Induction (Negative Charge)
Step 1: Bring Charged Object Near
Bring a positively charged conductor near the electroscope disk.
→ Charge redistribution occurs (electrostatic induction)
Qelectroscope = σ+A - σ-A
Step 2: Grounding (Touch the Base)
When touching the base, free electrons move from earth to electroscope
ΔQ = e- × n (where n is number of electrons)
→ The electroscope loses positive charges
Step 3: Remove Source Then Finger
After removing ground and charged object:
Qfinal = -|Qsource|
→ The electroscope becomes negatively charged
Practical Applications
- Charging objects in electrostatic painting systems
- Photocopying process in copy machines
- Air purification systems for suspended particles
- Charging balloons in educational experiments
Fundamental Conservation Law
ΣQbefore = ΣQafter
(Conservation of electric charge)
A process of charging a conductor without direct contact
Steps to charge an electroscope with negative charge by induction:
Bring a positively charged conductor near the electroscope (charge redistribution occurs in the electroscope)
Touch the electroscope base (grounding) - free charges not affected by attraction force dissipate
Remove your finger then remove the charged object - the electroscope becomes negatively charged
Charging by Contact
Scientific Explanation:
The process of transferring electric charge through direct contact between a charged object and a neutral one, where charges transfer until electrostatic equilibrium is reached.
Transfer Mechanism:
- If the object is negatively charged: excess electrons transfer to the neutral object
- If the object is positively charged: electrons are drawn from the neutral object
Practical Applications:
- Electrical grounding systems
- Rechargeable battery systems
- Wireless power transfer systems (via direct contact)
- Voltage measurement devices
Primary Purpose:
Equal distribution of electric charges between contacting objects, with control over the amount and type of transferred charge.
Coulomb's Law
Coulomb studied the mutual forces between electric charges
He studied the relationship between the electric force and the magnitudes of both charges while keeping the distance between them constant, as in the first experiment.
Then, he studied the relationship between the electric force and the distance between the charges while keeping the magnitudes of the charges constant, as in the second experiment.
Coulomb's Law Simulation
Relationship Between Force and Charge Magnitudes
Distance: 10 cm
5 μC
5 μC
Relationship Between Force and Distance
Distance: 10 cm
5 μC
5 μC
Experiment Results
-
Magnitude of Charges (q₁ and q₂):
The relationship is directly proportional to the product of the charges
Example: If one of the charges doubles → the force doubles
\[F\propto {q_1}{q_2}\]
-
Distance Between Them (r):
The relationship is inversely proportional to the square of the distance
Example: If the distance doubles → the force decreases to a quarter
\[F \propto \frac{1}{{{r^2}}}\]
-
Medium (k):
The electric permittivity depends on the medium:
k = 1/(4πε₀εᵣ)
where εᵣ is the relative permittivity of the medium
\[k = 8.99.0 \times {10^9}\frac{{{\rm{N}}{{\rm{m}}^{\rm{2}}}}{{{{\rm{C}}^{\rm{2}}}}}\]
Thus, he arrived at the following relationship:
\[F = k\frac{{{|𝑞_1 𝑞_2 |
}}}{{{r^2}}} \tag{1} \label{1}\]
\[k=1/4\pi\epsilon_0\]. Where \[\epsilon_0 = 8.85\times{10^{ - 12}}\frac{{{{\rm{C}}^{\rm{2}}}}}{{{\rm{N}}{{\rm{m}}^{\rm{2}}}}}\]
and is called the permittivity of free space.
Thus, Coulomb's equation can be written as follows:
\[F = \frac{1}{4𝜋ع_0}\frac{{{|𝑞_1 𝑞_2 |
}}}{{{r^2}}} \]
The force exerted between two point charges is a directional force and acts along the line connecting the two charges. This directional behavior leads to a vector representation of the force.
\[{{\vec F}_{21}}=-k\frac{q_1.q_2}{r^3}{{\vec r}_2}-{{\vec r}_1}=-k\frac{q_1.q_2}{r^2}.{ȓ}\]
Here, the type of charge is taken into account.
If the final result of the force is negative, it means the force is attractive.
If the final result of the force is positive, it means the force is repulsive.
In this simulation, the electric force between two charges is calculated by changing the magnitudes of the charges and the distance between them, and the electric force is calculated each time.
1
If an electric force from the first charge acts on the second charge
10N
to the right,
then the force exerted by the second charge on the first is equal to
Click here to show the solution
Choose the correct answer
1
If an electric force from the first charge acts on the second charge
10N
to the right
then the force exerted by the second charge on the first is equal to
Click here to show the solution method
Choose the correct answer
2
By what factor does the electric force between two charges change if the magnitude of one charge is doubled and the distance between them is halved
Click here to show the solution method
Choose the correct answer
3
Two charges have the same magnitude as shown in the figure. The distance
between them
0.2 m
If the electric force between
them is equal to
0.4 N
then the magnitude of each charge is equal to
Click here to show the solution method
Choose the correct answer
In the figure below, we have three electric charges
Determine the direction of the force acting on the first charge from the second charge and write the expression representing it
\[..........................................................\]
Click here to show the solution method
Determine the direction of the force acting on the first charge from the third charge and write the expression representing it
\[..........................................................\]
Click here to show the solution method
If the three charges are equal in magnitude, what is the direction of the force acting on the first charge
\[..........................................................\]
Click here to show the solution method
In this simulation, we place more than two charges next to each other and determine the force acting on one of the charges and the direction of the force
4
Three charges are in a straight line as shown in the figure, of the same type
and their magnitudes are shown in the figure. The direction of the force acting
on the charge
q2
Click here to show the solution
Choose the correct answer
5
( q1 ) The force acting on
was calculated to be 5 Newtons
and its direction is shown in the diagram
and the force acting
from
q3 on q1
equals 3 Newtons, then the second charge's magnitude and type
Click here to show the solution
Choose the correct answer
Charge Equilibrium
We say a charge is in equilibrium when the resultant force acting on the charge is zero
The two charges are of different types
The resultant force on a charge becomes zero if placed along the line connecting the two charges and closer to the smaller charge
\[F_{13}=F_{23}\]
Two charges of the same type
The resultant force on a charge becomes zero if placed along the line connecting the two charges and closer to the smaller charge
\[F_{13}=F_{23}\]
6
Two charges of different types but equal magnitude, determine at which location
if an electron is placed it won't be affected by an electric force
Click here to show the solution
Choose the correct answer
7
Two charged spheres with identical charges and same mass are suspended by inextensible
and massless strings so they repel each other with an electric force of magnitude
Fe = 4 N
where each string forms an angle \[𝜃 = 30^0\] with the vertical line, then the mass of each sphere
Click here to show the solution
Choose the correct answer
"The gravitational force between two bodies
"\[F = G\frac{{{m_1}{m_2}}}{{{r^2}}} \]
And the electrical force between two charges
\[F = k\frac{{{q_1}{q_2}}}{{{r^2}}} \]
Question: What are the similarities and differences between the two relationships without the results in the table
Electrostatic Forces - Part One |
The four fundamental forces of nature
Weak force |
Strong force |
Gravitational force |
Electromagnetic force |
|
|
|
|
Useful information:
Any atom consists of
a nucleus containing positively charged protons and neutral neutrons
Charge of proton = Charge of electron
𝑞𝑒 = 𝑞𝑝 = 1.602 X 10-19c
Electrons are what are gained or lost
Charged bodies contain protons and electrons but their numbers may be different
A negatively charged body has gained electrons
(Number of electrons > Number of protons
)
A positively charged body has lost electrons
(Number of protons > Number of electrons
)
The charge of a body can be expressed by knowing the number of protons and electrons in the body
using the following relation
A charged body has 32 more protons than electrons. The charge of the body is
equivalent to
Choose the correct answer A neutral body gained 8 electrons. The charge of the body is equivalent to
Choose the correct answer When rubbing a piece of wool with an ebonite rod,
the wool loses electrons and becomes positively charged and
the ebonite rod gains electrons and becomes negatively charged
Number of electrons lost by the wool = Number of electrons gained by the ebonite rod
(In a closed system)
A balloon was rubbed with a piece of wool and became negatively charged with a charge of
Choose the correct answer Millikan was able to prove that a charged oil droplet is charged with integer multiples of the charge of a single electron.
Using the Millikan oil-drop apparatus, the scientist was able to calculate the charge of the oil droplet.
When dividing the charge by the elementary charge, the result was an integer, confirming that charge is quantized.
1. Electric field
\[ (E) =\frac {V}{d}\] 2. Volume of spherical oil drop
\[ V = \frac {4}{3}πr³\] 3. Mass (m) = Density (ρ) × Volume (V) 4. Charge
\[(q) = \frac {(m × g × d)}{ V}\] 5. Number of electrons
\[(n) = \frac {q }{ e}\]
(where e = 1.6 × 10⁻¹⁹ coulombs) When examining protons and neutrons, it was found that they contain quarks with very small masses bound together by gluons.
Down quarks with negative charge Up quarks with positive charge \[-\frac{1}{3}e\] \[+\frac{2}{3}e\] .............................. : Solution A proton contains two up quarks and one down quark - determine the proton's charge
.............................. : Solution A neutron contains one up quark and two down quarks - determine the neutron's charge
These materials contain four valence electrons that form covalent bonds between atoms at absolute zero temperature (-273°C).
At absolute zero, they cannot conduct, but at room temperature some bonds break and they become conductive.
When doping semiconductors with impurities from Group 15 elements (N-type donors).
Doping is done with one impurity atom per million host atoms, making electrons the charge carriers.
When doping semiconductors with impurities from Group 13 elements (P-type acceptors).
Doping is done with one impurity atom per million host atoms, making holes the charge carriers.
Scientific Explanation:
Electromagnetic Interaction:
Generating static electric charges by transferring electrons between materials, maintaining the acquired charge for relatively long periods.
A process of separating electric charges in a conductor without direct contact with the charged object, where charges in the neutral body are affected by the electric field of the charged object. When bringing a negatively charged balloon near an aluminum can: Conductors: Contain free electrons in their outer atomic orbitals, allowing easy movement of electric charges through the material. Insulators: Have electrons tightly bound to their nuclei, preventing free movement and thus blocking electric current flow. When charging a conductor:
Insulators play crucial roles in:
Bring a positively charged conductor near the electroscope disk.
When touching the base, free electrons move from earth to electroscope
After removing ground and charged object:
ΣQbefore = ΣQafter
Scientific Explanation:
Transfer Mechanism:
Equal distribution of electric charges between contacting objects, with control over the amount and type of transferred charge.
Coulomb studied the mutual forces between electric charges
Thus, he arrived at the following relationship:
\[F = k\frac{{{|𝑞_1 𝑞_2 |
}}}{{{r^2}}} \tag{1} \label{1}\] \[k=1/4\pi\epsilon_0\]. Where \[\epsilon_0 = 8.85\times{10^{ - 12}}\frac{{{{\rm{C}}^{\rm{2}}}}}{{{\rm{N}}{{\rm{m}}^{\rm{2}}}}}\]
and is called the permittivity of free space.
Thus, Coulomb's equation can be written as follows:
\[F = \frac{1}{4𝜋ع_0}\frac{{{|𝑞_1 𝑞_2 |
}}}{{{r^2}}} \]
The force exerted between two point charges is a directional force and acts along the line connecting the two charges. This directional behavior leads to a vector representation of the force.
\[{{\vec F}_{21}}=-k\frac{q_1.q_2}{r^3}{{\vec r}_2}-{{\vec r}_1}=-k\frac{q_1.q_2}{r^2}.{ȓ}\]
Here, the type of charge is taken into account.
If the final result of the force is negative, it means the force is attractive.
If the final result of the force is positive, it means the force is repulsive.
If an electric force from the first charge acts on the second charge
Choose the correct answer If an electric force from the first charge acts on the second charge
Choose the correct answer By what factor does the electric force between two charges change if the magnitude of one charge is doubled and the distance between them is halved
Choose the correct answer Two charges have the same magnitude as shown in the figure. The distance
between them
Choose the correct answer In the figure below, we have three electric charges
Determine the direction of the force acting on the first charge from the second charge and write the expression representing it
Determine the direction of the force acting on the first charge from the third charge and write the expression representing it
\[..........................................................\]
If the three charges are equal in magnitude, what is the direction of the force acting on the first charge
\[..........................................................\]
Three charges are in a straight line as shown in the figure, of the same type
Choose the correct answer ( q1 ) The force acting on Choose the correct answer We say a charge is in equilibrium when the resultant force acting on the charge is zero
The two charges are of different types
The resultant force on a charge becomes zero if placed along the line connecting the two charges and closer to the smaller charge
\[F_{13}=F_{23}\] Two charges of the same type
The resultant force on a charge becomes zero if placed along the line connecting the two charges and closer to the smaller charge
\[F_{13}=F_{23}\] Two charges of different types but equal magnitude, determine at which location
if an electron is placed it won't be affected by an electric force
Choose the correct answer Two charged spheres with identical charges and same mass are suspended by inextensible
and massless strings so they repel each other with an electric force of magnitude
Choose the correct answer "The gravitational force between two bodies "\[F = G\frac{{{m_1}{m_2}}}{{{r^2}}} \]
and negatively charged electrons orbiting around it in elliptical orbits
The atom is electrically neutral?
Number of protons = Number of electrons
Click here to show solution
Click here to show solution
8 X 10-19c
Then the piece of wool has lost
Click here to show solution
Millikan Oil Drop Experiment
Formulas Used:
Solved Example
Given that the molar mass of iron
\[56\;g\] and its atomic number is 26
Solution Method:
Every 1 mole of any substance contains Avogadro's number of atoms
6.022 X 1023 atoms
One mole of iron has a mass of 56 grams
First calculate the number of atoms in 1.4 kg mass
\[N=\frac{6.022×10^{23}×1.4×10^3}{56}= 1.5055 × 10^{25}\]
The atomic number is the number of protons in the atom (number of protons = number of electrons) for iron atom = 26
Number of electrons in 1.4 kg mass
\[N= 26 ×1.5055 × 10^{25}= 3.9143 × 10^{26}\]
The ratio of gained electrons is the number of gained electrons to the total number of electrons
To calculate the number of gained electrons
\[n=\frac{0.4}{1.6× 10^{-19}}= 2.5× 10^{18}\]
To calculate the ratio of gained electrons
\[\frac{2.5× 10^{18}}{3.9143 × 10^{26}}=6.38 × 10^{-9}\]
Conductors, Insulators, Semiconductors and Superconductors
Insulators:
Materials that cannot conduct electric current because their electrons are bound to the nucleus and cannot move through the material like wood, plastic, and ebonite.
Semiconductors: Materials that can conduct current under special conditions like germanium and silicon (Group 14 elements).
Superconductors:
Materials with almost zero resistance to current flow, which only work at very low temperatures like titanium.
Types of Electric Charging
Charging by Friction
This phenomenon occurs when two different objects are rubbed together, causing electrons to transfer from one object to another due to differences in materials' electron affinity.
- Material with higher electron affinity (like wool) loses electrons
- Material with lower electron affinity (like plastic) gains electrons
Practical Applications:
Primary Purpose:
Charging by Induction
Definition:
Process Steps:
Practical Example:
Key Characteristics:
Comparison Between Charging Conductors and Insulators
Property
Conductors
Insulators
Electron Movement
Free-moving electrons
Bound electrons
Electrical Conduction
✅ Excellent conduction
❌ No conduction
Thermal Conduction
✅ Good heat conduction
❌ Poor heat conduction
Examples
Copper, silver, aluminum
Wood, glass, rubber
Surface Charging
Charges spread on surface
Charges remain localized
Applications
Electrical wiring
Wire insulation
Scientific Explanation:
Charge Conservation Law:
- Charges move to the outer surface
- Charges distribute evenlyEnvironmental Impact:
- Preventing electric shocks
- Maintaining current stability
- Reducing energy loss
When bringing a charged object near a conductor, charge redistribution occurs, while in insulators the positive and negative charge centers separate without movement
Charging an Electroscope by Induction (Negative Charge)
Step 1: Bring Charged Object Near
→ Charge redistribution occurs (electrostatic induction)
Qelectroscope = σ+A - σ-A
Step 2: Grounding (Touch the Base)
ΔQ = e- × n (where n is number of electrons)
→ The electroscope loses positive charges
Step 3: Remove Source Then Finger
Qfinal = -|Qsource|
→ The electroscope becomes negatively charged
Practical Applications
Fundamental Conservation Law
(Conservation of electric charge)
A process of charging a conductor without direct contact
Steps to charge an electroscope with negative charge by induction:
Bring a positively charged conductor near the electroscope (charge redistribution occurs in the electroscope)
Touch the electroscope base (grounding) - free charges not affected by attraction force dissipate
Remove your finger then remove the charged object - the electroscope becomes negatively charged
Charging by Contact
The process of transferring electric charge through direct contact between a charged object and a neutral one, where charges transfer until electrostatic equilibrium is reached.
- If the object is negatively charged: excess electrons transfer to the neutral object
- If the object is positively charged: electrons are drawn from the neutral object
Practical Applications:
Primary Purpose:
He studied the relationship between the electric force and the magnitudes of both charges while keeping the distance between them constant, as in the first experiment.
Then, he studied the relationship between the electric force and the distance between the charges while keeping the magnitudes of the charges constant, as in the second experiment.
Relationship Between Force and Charge Magnitudes
Relationship Between Force and Distance
5 μC
5 μC
Experiment Results
The relationship is directly proportional to the product of the charges
Example: If one of the charges doubles → the force doubles
\[F\propto {q_1}{q_2}\]
The relationship is inversely proportional to the square of the distance
Example: If the distance doubles → the force decreases to a quarter
\[F \propto \frac{1}{{{r^2}}}\]
The electric permittivity depends on the medium:
k = 1/(4πε₀εᵣ)
where εᵣ is the relative permittivity of the medium
\[k = 8.99.0 \times {10^9}\frac{{{\rm{N}}{{\rm{m}}^{\rm{2}}}}{{{{\rm{C}}^{\rm{2}}}}}\]
In this simulation, the electric force between two charges is calculated by changing the magnitudes of the charges and the distance between them, and the electric force is calculated each time.
10N
to the right,
then the force exerted by the second charge on the first is equal to
Click here to show the solution
10N
to the right
then the force exerted by the second charge on the first is equal to
Click here to show the solution method
Click here to show the solution method
0.2 m
If the electric force between
them is equal to
0.4 N
then the magnitude of each charge is equal to
Click here to show the solution method
\[..........................................................\]
Click here to show the solution method
Click here to show the solution method
Click here to show the solution method
and their magnitudes are shown in the figure. The direction of the force acting
on the charge
q2
Click here to show the solution
was calculated to be 5 Newtons
and its direction is shown in the diagram
and the force acting
from
q3 on q1
equals 3 Newtons, then the second charge's magnitude and type
Click here to show the solution
Charge Equilibrium
Click here to show the solution
Fe = 4 N
where each string forms an angle \[𝜃 = 30^0\] with the vertical line, then the mass of each sphere
Click here to show the solution
And the electrical force between two charges
\[F = k\frac{{{q_1}{q_2}}}{{{r^2}}} \]
Question: What are the similarities and differences between the two relationships without the results in the table
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