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Electric Charges and Fields - Chapter One
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Electric Charges and Fields - Chapter One

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@SuaveElation8602

Questions and Answers

What is the formula for the magnitude of the force between two point charges in vacuum?

F = k * (q1 * q2) / r^2

Who developed Coulomb's law?

Charles Augustin de Coulomb

What is the value of the constant k in Coulomb's law in SI units?

k = 9 × 10^9 Nm^2/C^2

What is the permittivity of free space denoted as in Coulomb's law?

<p>ε0</p> Signup and view all the answers

Coulomb's law applies only when charges are in a vacuum.

<p>False</p> Signup and view all the answers

What happens to the force between two charges when the distance between them is halved?

<p>The force becomes four times greater.</p> Signup and view all the answers

What is Coulomb's law expressed in vector notation?

<p>F21 = (1 / (4πε0)) * (q1 * q2) / r21^2</p> Signup and view all the answers

What principle allows the calculation of force on a charge due to several charges?

<p>The principle of superposition.</p> Signup and view all the answers

What is the total force F1 on charge q1 due to all other charges?

<p>F1 = sum of F12, F13, ..., F1n</p> Signup and view all the answers

What is the formula for the electric field E produced by charge Q at a point r?

<p>E(r) = (1 / (4πε0)) * (Q / r^2) r̂</p> Signup and view all the answers

What does the electric field E due to charge Q represent?

<p>The force experienced by a unit positive charge placed at that point</p> Signup and view all the answers

The magnitude of the electric field E produced by a charge is independent of the distance from the charge.

<p>False</p> Signup and view all the answers

In an equilateral triangle with charges at each vertex, what is the resultant force on the charge at the centroid?

<p>0</p> Signup and view all the answers

What happens to the direction of the electric field when the source charge is negative?

<p>The electric field vector points radially inwards.</p> Signup and view all the answers

How is the electric field E defined operationally?

<p>As the ratio of force to charge placed in the field</p> Signup and view all the answers

What law describes the interaction between two point charges?

<p>Coulomb's law</p> Signup and view all the answers

The electric field is a characteristic of the test charge placed at a point.

<p>False</p> Signup and view all the answers

What is the result of the forces acting on charges at the vertices of an equilateral triangle when the charges are identical?

<p>The sum of the forces is zero.</p> Signup and view all the answers

What is the SI unit of electric field?

<p>N/C</p> Signup and view all the answers

What is the phenomenon experienced when taking off synthetic clothes in dry weather?

<p>Static electricity discharge</p> Signup and view all the answers

Who historically discovered that amber rubbed with wool attracts light objects?

<p>Thales of Miletus</p> Signup and view all the answers

Like charges attract each other.

<p>False</p> Signup and view all the answers

What are the two kinds of charges known?

<p>Positive and negative</p> Signup and view all the answers

What device is used to detect charge on a body?

<p>Gold-leaf electroscope</p> Signup and view all the answers

Which of the following substances is a conductor?

<p>Copper</p> Signup and view all the answers

What happens to the charges on a conductor when it is charged?

<p>Charges distribute over the entire surface.</p> Signup and view all the answers

What is the basic unit of charge in the International System (SI) of Units?

<p>Coulomb</p> Signup and view all the answers

The charge on an electron is written as ______.

<p>-e</p> Signup and view all the answers

What happens to electric charge when two electrified bodies come in contact?

<p>The charges neutralize each other.</p> Signup and view all the answers

Which process leads to the transfer of electrons from one body to another?

<p>Electrification by rubbing</p> Signup and view all the answers

What is the unit of electric flux?

<p>N C–1 m2</p> Signup and view all the answers

What is an electric dipole?

<p>A pair of equal and opposite point charges separated by a distance.</p> Signup and view all the answers

Which direction defines the dipole?

<p>From -q to +q</p> Signup and view all the answers

What is the equation for the time required by the electron to fall through a distance h?

<p>t_e = \frac{2h m_e}{eE}</p> Signup and view all the answers

The electric field of an electric dipole is zero.

<p>False</p> Signup and view all the answers

What happens to the electric field of a dipole at large distances?

<p>It falls off as $1/r^3$.</p> Signup and view all the answers

What is the mass of the electron, denoted as m_e?

<p>9.11 × 10–31 kg</p> Signup and view all the answers

What is the value of the electric field strength E given in the document?

<p>2.0 × 10^4 N C–1</p> Signup and view all the answers

What is the dipole moment vector defined as?

<p>p = q × 2a p̂</p> Signup and view all the answers

What is a point dipole?

<p>A dipole where the size approaches zero and charge approaches infinity such that the product remains finite.</p> Signup and view all the answers

What is the time of fall for the electron, denoted as t_e?

<p>2.9 × 10–9 s</p> Signup and view all the answers

What is the mass of the proton, denoted as m_p?

<p>1.67 × 10–27 kg</p> Signup and view all the answers

In the presence of an electric field, polar molecules have:

<p>Both B and C</p> Signup and view all the answers

What is the torque on a dipole in a uniform external electric field?

<p>τ = p × E</p> Signup and view all the answers

What is the equation for the acceleration of the proton?

<p>a_p = \frac{eE}{m_p}</p> Signup and view all the answers

What happens when a dipole is parallel to an external electric field?

<p>It experiences a net force in the direction of increasing field.</p> Signup and view all the answers

What is the time of fall for the proton, denoted as t_p?

<p>1.3 × 10–7 s</p> Signup and view all the answers

What is the calculated acceleration of the proton in the electric field?

<p>1.9 × 10^12 m s–2</p> Signup and view all the answers

What are the magnitudes of the electric fields E1A and E2A at point A due to the charges?

<p>E1A = 3.6 × 10^4 N C–1 and E2A = 3.6 × 10^4 N C–1</p> Signup and view all the answers

What is the total electric field E_A at point A?

<p>E_A = 7.2 × 10^4 N C–1</p> Signup and view all the answers

What is the direction of the total electric field at point A?

<p>Directed towards the right</p> Signup and view all the answers

What is the relationship between the density of electric field lines and the strength of the electric field?

<p>The density of field lines indicates the strength of the electric field.</p> Signup and view all the answers

Electric field lines form closed loops.

<p>False</p> Signup and view all the answers

Field lines can intersect each other.

<p>False</p> Signup and view all the answers

Electric flux through an area element DS is defined by Df = E . DS = E DS cos______.

<p>q</p> Signup and view all the answers

What does the charged comb induce in the piece of paper?

<p>A net dipole moment</p> Signup and view all the answers

The electric field due to the comb is uniform.

<p>False</p> Signup and view all the answers

What is surface charge density represented as?

<p>σ</p> Signup and view all the answers

What are the units for surface charge density?

<p>C/m²</p> Signup and view all the answers

How is linear charge density defined?

<p>λ = ∆Q/∆l</p> Signup and view all the answers

What are the units for linear charge density?

<p>C/m</p> Signup and view all the answers

What is volume charge density represented as?

<p>ρ</p> Signup and view all the answers

What are the units for volume charge density?

<p>C/m³</p> Signup and view all the answers

How can the electric field due to a continuous charge distribution be obtained?

<p>Using Coulomb's law and the superposition principle</p> Signup and view all the answers

What distance is between the charge element and a point P in the charge distribution?

<p>r'</p> Signup and view all the answers

What is the relationship used to sum the electric fields due to different volume elements?

<p>E ≅ Σ (ρ ΔV / (4πε₀ r'²))</p> Signup and view all the answers

Study Notes

Electric Charges and Fields

  • Static Electricity: Common experiences like sparks from synthetic clothing or lightning during thunderstorms are manifestations of static electricity, where charges accumulate due to rubbing insulating surfaces.

  • Electric Charge History: The phenomenon of certain materials attracting light objects upon being rubbed dates back to Thales of Miletus in 600 BC. The term "electricity" comes from "elektron," the Greek word for amber.

  • Types of Charges: There are two types of electric charges:

    • Positive Charge: Acquired by materials like glass when rubbed with silk.
    • Negative Charge: Acquired by materials like silk when rubbed with glass.

  • Charge Interaction:

    • Like charges repel each other.
    • Unlike charges attract each other.

  • Charge Neutralization: When a charged body contacts another charged body of opposite charge, they neutralize each other, demonstrating the observable behavior of charges.

  • Detection of Charges: A gold-leaf electroscope can indicate charge presence. When a charged object touches its metal knob, charge flows into the gold leaves, causing them to diverge.

Conductors and Insulators

  • Conductors: Materials that allow electricity to pass freely include metals, human and animal bodies, and the earth. They have free-moving electrons.

  • Insulators: Materials like glass, porcelain, plastic, and wood resist electric flow. Charges on insulators remain localized, while charges on conductors distribute evenly.

  • Charging Mechanism: Rubbing transfers electrons, allowing materials to gain positive or negative charge, but conservation of charge means no new charge is created.

Properties of Electric Charge

  • Additivity of Charges: Total charge is found by algebraically adding individual charges. Charge behaves as a scalar quantity, having magnitude but no direction.

  • Conservation of Charge: Charge cannot be created or destroyed in an isolated system. Interactions may lead to redistribution, but the total charge remains constant.

  • Quantisation of Charge: Electric charge exists in discrete units, with charge values always being integral multiples of a basic unit denoted as ( e ) (approximately ( 1.602 \times 10^{-19} ) C).

  • Coulomb's Law: Defines the interaction force ( F ) between two point charges ( q_1 ) and ( q_2 ) separated by a distance ( r ) as:

    • ( F = k \frac{q_1 q_2}{r^2} ) Where ( k ) is Coulomb's constant.

Key Concepts in Coulomb's Law

  • Experimental Research: Developed using a torsion balance, allowing Coulomb to examine forces between charged spheres methodically by varying distances and measuring force.

  • Charge Distribution: When identical uncharged spheres contact a charged sphere, the charge distributes evenly, illustrating methods for understanding charge behavior in small systems.

Practical Implications

  • Coulomb Charge Example: It takes approximately 200 years to accumulate a charge of 1 coulomb from a body losing ( 10^9 ) electrons per second, highlighting the scale of elementary charge.

  • Molecular Charge Composition: A cup of water (~250 g) consists of numerous molecules, each contributing to equal positive and negative charge distributions, demonstrating everyday applications of electric charge principles.### Coulomb's Law and Experimental Foundations

  • Coulomb's Law describes the electrostatic force between charged particles and was formulated by Charles-Augustin de Coulomb.

  • A torsion balance, invented for measuring forces, was key in establishing the empirical basis for Coulomb's Law.

  • The law applies to both macroscopic and subatomic scales, with distances down to approximately ( r \sim 10^{-10} ) m.

Definition and Calculation of Charge

  • Coulomb's Law can define a unit of electric charge based on the magnitude of forces measured.
  • The dimensionless constant ( k ) in the law can be chosen arbitrarily, influencing the unit of charge.
  • In SI units, ( k ) is approximately ( 9 \times 10^9 , \text{N m}^2/\text{C}^2 ) leading to the definition of the coulomb (C) as the charge producing a force of ( 9 \times 10^9 , \text{N} ) at a distance of ( 1 , \text{m} ).

Mathematical Representation

  • The formula for Coulomb’s force is expressed as: [ F = \frac{k q_1 q_2}{r^2} ]
  • This can be reformulated using permittivity of free space ( \epsilon_0 ): [ F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} ]
  • Value of ( \epsilon_0 ) in SI units is approximately ( 8.854 \times 10^{-12} , \text{C}^2 \text{N}^{-1}\text{m}^{-2} ).

Vector Form of Coulomb's Law

  • The law is typically represented in vector form to indicate directionality of forces: [ \mathbf{F}{21} = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2 \hat{r}{21}}{r_{21}^2} ]
  • Forces are attractive if charges are of opposite sign and repulsive if of the same sign.

Superposition Principle

  • The principle of superposition allows for calculation of the net force on a charge due to multiple other charges by vector summing individual forces.
  • No charge’s presence affects the electrostatic force exerted on another charge.

Comparisons Between Forces

  • Electric forces, as shown in examples, greatly exceed gravitational forces; electric force between an electron and a proton shows a ratio of ( 2.4 \times 10^{39} ) compared to gravitational force.
  • Given the electric force values when charges are separated by ( 1 , \text{Å} ), an electron undergoes accelerations on the order of ( 2.5 \times 10^{22} , \text{m/s}^2 ), vastly overshadowing gravitational effects.

Impact of Charge Redistribution

  • When conductive spheres touch, charges redistribute evenly, which retains the overall electrostatic force regardless of distance changes when using Coulomb’s law.
  • Example calculations illustrate identical electrostatic forces post redistribution if the distance is halved.

Forces in Multiple Charge Systems

  • For systems with multiple charges, the net force on a charge is the vector sum of all other charges’ influences.
  • The forces can be calculated individually and combined using vector addition principles.

Specific Scenarios with Charged Configurations

  • In the case of three equal charges arranged in an equilateral triangle, the net force on a charge at the centroid results in zero due to symmetry.
  • Consideration of force directions and magnitudes demonstrates the complexity of electrostatic interactions in multi-charge systems.### Forces on Charges
  • The sum of forces on three charges is zero, indicating equilibrium: F1 + F2 + F3 = 0.
  • Coulomb’s law aligns with Newton's third law of motion, confirming mutual force interactions.

Electric Field

  • A point charge Q creates an electric field in the surrounding space even when not tested against another charge.
  • The electric field E at a distance r from charge Q is expressed as:
    E(r) = (1 / (4πε₀)) * (Q / r²) * r̂.
  • The unit vector r̂ indicates direction from the origin to the point where the field is evaluated.

Force from Electric Field

  • The force F on a test charge q within the electric field is given by:
    F = q * E(r).
  • Electric field E is defined independently from the test charge q.

Characteristics of Electric Field

  • Defined as the force experienced by a unit positive charge at any point in space due to surrounding source charges.
  • Electric field E is a vector field; its strength and direction vary depending on the position in relation to source charges.
  • Positive charge creates a field that radiates outwards; negative charge's field points inwards.
  • Electric field possesses spherical symmetry around point charges, remaining constant at equal distances.

Superposition Principle

  • For multiple charges, the resultant electric field at a point is the vector sum of the fields due to individual charges.
  • Expressed mathematically as:
    E(r) = Σ (qi / (4πε₀ * r²i)) * r̂iP for i = 1 to n.

Significance of Electric Field

  • Electric fields provide insight into electrical environments without needing to directly observe forces on test charges.
  • Changes in electric fields, especially in dynamic situations, account for time delays in interactions due to the finite speed of light.

Examples

  • An electron in an electric field experiences acceleration based on its charge and mass:
    a_e = (eE) / m_e.
  • The electron falls through 1.5 cm under acceleration much greater than that of gravitational forces, resulting in negligible gravitational effects.
  • Comparing electron and proton dynamics in an electric field reveals differing fall times due to their mass differences.

Electric Field Lines

  • Electric field strength can be visually represented using field lines; density of lines corresponds to field strength.
  • Lines point radially from charges, with proximity indicating strength: denser near the source, less dense further away.
  • Field lines are a conceptual tool to understand electric fields’ spatial properties and interactions.

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Explore the fundamental concepts of electric charges and fields in this engaging quiz based on Chapter One. Understand the phenomena of static electricity, sparks, and electric discharges like lightning through a series of insightful questions. Prepare to challenge your knowledge and learn something new!

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