Electrostatics

Electrostatics is the branch of physics that studies electric charges at rest.

The force between two unit-positive charges separated by 1 meter is defined by Coulomb's constant, \(k_e\).

Coulomb's law resembles Newton's Law of Gravitation as both describe forces that act over a distance and follow an inverse-square law.

The electrostatic force between two protons at the same distance would also be \(F\) because both electrons and protons have the same magnitude of charge.

The direction of the electric force and electric field intensity are parallel to each other.

The work done on a unit charge against an electric field is known as electric potential.

Capacitance increases when capacitors are connected in parallel because the total surface area for charge storage increases.

When two capacitors of 8µF are connected in series, the equivalent capacitance is given by \( \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \), resulting in 4 µF.

The presence of a dielectric between the plates of a capacitor increases its capacitance because the dielectric reduces the electric field between the plates.

Doubling the area of a parallel plate capacitor will double its capacitance, as capacitance is directly proportional to the area of the plates.

Electrostatic induction is the process of charging a body without direct contact. This occurs when a charged object is brought near a neutral object, causing a redistribution of charge within the neutral object.

An electroscope is used to detect the presence of an electric charge. It works on the principle of electrostatic induction and repulsion.

According to Coulomb's Law, the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, \( F = k \frac{q_1 q_2}{r^2} \).

The electric field is defined as the area around a charge where it exerts an electric force on other charges.

Electric intensity, or electric field strength, measures the force per unit charge exerted on a charge placed in an electric field.

Electrostatic potential is the work needed to move a unit positive charge from a reference point to a specific point against an electric field.

The SI unit of electric potential and potential difference is the Volt (V).

A capacitor is an electronic component that stores electric charge. It is used in various applications, including energy storage and filtering.

In a series combination of capacitors, the total capacitance is given by the reciprocal of the sum of the reciprocals of individual capacitances: \( \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots \).

In a parallel combination of capacitors, the total capacitance is equal to the sum of the individual capacitances: \( C_{\text{total}} = C_1 + C_2 + \cdots \).

The value of 1 electron volt in joules is approximately \( 1.602 \times 10^{-19} \) J.

Small Van de Graaff generators are primarily used in schools to demonstrate the behavior of static charges and principles of electrostatics.

A neutron is a neutral particle, meaning it has no electric charge.

The unit of electric charge in the SI system is the Coulomb (C).

Induction is the method of charging an object without touching it, using the influence of nearby charges.

Like charges repel each other due to electrostatic forces.

The charge on a single electron is approximately \( -1.602176634 \times 10^{-19} \) coulomb.

The triboelectric effect is related to static electricity, where certain materials become electrically charged after coming into contact with another material and then separating.

The formula to calculate charge in terms of current and time is \( Q = I \times t \), where \( Q \) is the charge, \( I \) is the current, and \( t \) is the time.

"Charges are quantized" means that electric charge exists in discrete units, with the elementary charge being approximately \( e = 1.6 \times 10^{-19} \) coulombs.

The main purpose of an electroscope is to detect the presence of electric charge.

The principle behind the working of an electroscope is electrostatic force, which causes the leaves to repel each other when charged.

The metal leaves of an electroscope diverge due to the repulsion of like charges when a charged object is brought near or touches the electroscope.

An electrometer is used for the quantitative measurement of electric charge.

Coulomb’s Law explains the force between electrically charged bodies.

According to Coulomb’s Law, the force between two point charges is directly proportional to the product of the magnitudes of the charges.

According to Coulomb’s Law, the force between two point charges is inversely proportional to the square of the distance between them.

The correct formula of Coulomb’s Law is \( F = k \frac{q₁ q₂}{r^2} \), where \( F \) is the force, \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between the charges.

The value of the constant in Coulomb’s law is approximately \( 9.0 \times 10^9 \, \text{N·m²/C²} \).

The symbol \( \epsilon_0 \) represents the permittivity of free space, a constant used in Coulomb's Law.

The value of \( \epsilon_0 \) is approximately \( 8.85 \times 10^{-12} \, \text{C²/N·m²} \).

An electric field is a region around a charge where an electrostatic force is exerted on other charges.

Michael Faraday gave the concept of the electric field.

The SI unit of electric field intensity is Newton per Coulomb (N/C).

The formula of electric field intensity is \( E = \frac{F}{Q} \), where \( E \) is the electric field intensity, \( F \) is the force, and \( Q \) is the charge.

Electric field lines point outwards around a positive charge.

A test charge is a very small charge that is used to measure the electric field without significantly affecting it.

The value of the elementary charge \( e \) is approximately \( 1.602176634 \times 10^{-19} \, \text{C} \).

The force between two like charges is repulsion.

The electric field intensity is given by \( E = \frac{F}{Q} \). For a force of 9 µN and a charge of 3 µC, \( E = \frac{9 \times 10^{-6} \, \text{N}}{3 \times 10^{-6} \, \text{C}} = 3 \, \text{N/C} \).

Electrostatic potential is defined as the work done to move a unit positive charge from a reference point to a specific point without acceleration.

The SI unit of electrostatic potential is the Volt (V).

As electrons move from a negative to a positive charge, they gain potential energy.

When moving through a conductor, electrons lose potential energy.

The formula for electric potential \( V \) is \( V = \frac{W}{Q} \), where \( W \) is the work done and \( Q \) is the charge.

The potential difference is given by \( V = \frac{W}{Q} \). For 300 mJ of work and a 150 mC charge, \( V = \frac{300 \times 10^{-3} \, \text{J}}{150 \times 10^{-3} \, \text{C}} = 2 \, \text{V} \).

Electric current naturally flows from higher electric potential to lower electric potential.

Potential difference is also commonly referred to as voltage.

An electrostatic air purifier uses electrostatics to clean air by charging particles and collecting them on oppositely charged plates.

The unit of capacitance is the Farad (F).

An insulating material is placed between the plates of a capacitor to form a dielectric, which increases the capacitor's ability to store charge.

The relationship between charge \( Q \), capacitance \( C \), and voltage \( V \) is given by the equation \( Q = CV \).

Capacitance is directly proportional to the area of the plates. Larger plate area results in greater capacitance.

Capacitance is inversely proportional to the distance between the plates. Increasing the distance between the plates decreases the capacitance.

When a dielectric is inserted between the plates of a capacitor, the capacitance increases due to the dielectric constant of the material.

The capacitance of a capacitor becomes half if the dielectric is removed, as the dielectric constant affects the capacitance.

The equivalent capacitance of capacitors connected in parallel is the sum of their individual capacitances. For four 1 μF capacitors, the total capacitance is \( 1 + 1 + 1 + 1 = 4 \, \mu\text{F} \).

In a parallel combination of capacitors, the voltage remains the same across each capacitor.

In a series combination of capacitors, the charge remains the same across all capacitors.

The formula for total capacitance in a series combination of capacitors is \( \frac{1}{C} = \frac{1}{C₁} + \frac{1}{C₂} + \frac{1}{C₃} \).

The dielectric constant affects the capacitance of a capacitor by increasing it.

The energy stored in a capacitor is given by \( E = \frac{1}{2} CV^2 \), where \( C \) is the capacitance and \( V \) is the voltage.

Producing AC voltage is not a common use of capacitors. Capacitors are typically used for tuning radios, running fans, and signal filtering.