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What is the vector leading from 1 to 2 denoted as?
r21
What is the magnitude of the vector r21 denoted by?
r21
Coulomb's force law between two point charges q1 and q2 located at r1 and r2, respectively is expressed as?
Coulomb’s law agrees with Newton’s third law.
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The ratio of the magnitudes of electric force to gravitational force between an electron and a proton is ________.
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What is the magnitude of the electric force between two protons compared to the gravitational force?
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What is the study of forces, fields, and potentials arising from static charges called?
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Charge on a body is always positive.
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What is the name of the scientist who coined the term 'electricity'?
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When we rub a glass rod with silk, the rod gets __________ charged and the silk gets negatively charged.
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What is the formula for the total force on charge q1, F1, due to all other charges?
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In a system of charges, what does the electric field at a point in space represent?
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Define the electric field produced by a charge Q at a point r.
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Electric field due to a point charge is dependent on the test charge used to measure it.
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Who first suggested the quantisation of charge?
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What is the SI unit of charge?
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One coulomb is defined as the charge flowing through a wire in 1 s if the current is 1 ___.
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Charge can increase or decrease in steps of e at the macroscopic level.
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Match the following components with their respective values in the International System of Units (SI):
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What is the expression for electric field E2 at point P due to charge q2?
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What is the vector sum of electric fields at a point due to a system of charges?
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What is the significance of the concept of electric field in physics?
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The acceleration of an electron falling in a uniform electric field is given by ae = eE/me, where e is charge of electron and me is its _____________.
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In the example provided, the electric field at point B is directed towards the right.
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What is the formula for calculating electric field along the dipole axis?
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What is the direction of the electric field when the dipole moment vector is opposite to the electric field?
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What is the torque equation for a dipole in a uniform external field?
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How is surface charge density defined?
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Continuous charge distribution can be treated in the same way as discrete charges.
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What is important when estimating the density of field lines?
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What does the relative density of field lines indicate?
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Field lines crowd where the field is weak.
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The solid angle is a measure of a ____. (Fill in the blank)
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Match the following properties of electric field lines with their descriptions:
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What is the definition of electric flux?
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What is an electric dipole?
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The __________ defines a direction in space for an electric dipole.
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The total charge of an electric dipole is zero.
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What is the formula to calculate the electric field at a point on the axis of an electric dipole?
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Study Notes
Electric Charges and Fields
- Electric charges are static, meaning they do not move or change with time.
- Electrostatics deals with the study of forces, fields, and potentials arising from static charges.
Electric Charge
- Thales of Miletus discovered that rubbing amber with wool or silk cloth attracts light objects.
- The name "electricity" is derived from the Greek word "elektron", meaning amber.
- There are two kinds of electric charges: positive and negative.
- Like charges repel each other, while unlike charges attract each other.
- The property that differentiates the two kinds of charges is called the polarity of charge.
- When a body is rubbed with another, electrons are transferred, resulting in one body becoming positively charged and the other negatively charged.
- The charges acquired after rubbing are lost when the charged bodies are brought in contact.
Conductors and Insulators
- Conductors are substances that allow electricity to pass through them easily, such as metals, human and animal bodies, and earth.
- Insulators are substances that do not allow electricity to pass through them easily, such as glass, porcelain, plastic, and wood.
- When a charge is transferred to a conductor, it is distributed over the entire surface of the conductor.
- When a charge is put on an insulator, it stays at the same place.
Basic Properties of Electric Charge
- Electric charges are scalar quantities, having magnitude but no direction.
- Charges add up like real numbers, and they can be either positive or negative.
- The total charge of a system is conserved, meaning it is not possible to create or destroy net charge carried by an isolated system.
- Electric charge is quantized, meaning it exists in discrete units, which are multiples of the basic unit of charge e.
- The basic unit of charge e is defined as the charge that an electron or proton carries.
- The quantization of charge was first suggested by the experimental laws of electrolysis and experimentally demonstrated by Millikan in 1912.
Coulomb's Law
- Coulomb's Law is a quantitative statement about the force between two point charges.
- The force between two point charges is directly proportional to the product of the magnitude of the two charges and inversely proportional to the square of the distance between the charges.
- The force acts along the line joining the two charges.
- Coulomb used a torsion balance to measure the force between two charged metallic spheres and discovered the relation between the force, charges, and distance.### Coulomb's Law and Electric Force
- Coulomb's law is a fundamental principle in electrostatics that describes the electric force between two charged objects.
- The law was discovered by Charles-Augustin de Coulomb in 1785 and is a simple mathematical statement that relates the electric force between two charges to the distance between them.
Key Features of Coulomb's Law
- The law states that the electric force between two charges is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
- The constant of proportionality, k, is a universal constant that depends on the units used to measure the charge and distance.
- In SI units, the value of k is approximately 9 × 10^9 N m^2/C^2.
- The unit of charge that results from this choice is called a coulomb (C), which is defined as the charge that, when placed at a distance of 1 m from another charge of the same magnitude in vacuum, experiences an electrical force of repulsion of magnitude 9 × 10^9 N.
Electric Force Between Two Charges
- The electric force between two charges is a vector that acts along the line joining the two charges.
- The magnitude of the force is given by Coulomb's law: F = k * q1 * q2 / r^2, where q1 and q2 are the magnitudes of the charges, and r is the distance between them.
- The direction of the force is given by the unit vector r̂, which points from one charge to the other.
Vector Notation
- The electric force between two charges can be written in vector notation as F21 = k * q1 * q2 * r̂21 / r21^2, where r̂21 is the unit vector from charge 2 to charge 1.
- The force on charge 1 due to charge 2 is opposite in direction to the force on charge 2 due to charge 1, as required by Newton's third law.
Electric Force in Matter
- Coulomb's law is valid only in vacuum and does not apply in matter, where the electric force is modified by the presence of other charged particles.
- In matter, the electric force between two charges is reduced by a factor ε, known as the permittivity of the material.
Principle of Superposition
- The electric force on a charge due to multiple other charges is the vector sum of the forces due to each charge individually.
- This is known as the principle of superposition, which is a fundamental principle in electrostatics.
Examples of Electric Force
- Example 1.3: Compare the strength of electric and gravitational forces between two charges and two masses, respectively.
- Example 1.4: A charged metallic sphere is suspended by a nylon thread, and another charged metallic sphere is brought close to it. What is the expected repulsion of the first sphere?
- Example 1.5: Consider three charges q1, q2, and q3 each equal to q at the vertices of an equilateral triangle. What is the force on a charge Q (with the same sign as q) placed at the centroid of the triangle?
- Example 1.6: Consider the charges q, q, and –q placed at the vertices of an equilateral triangle. What is the force on each charge?### Electric Forces and Fields
- The sum of forces on three charges is zero, which is a result of Coulomb's law being consistent with Newton's third law.
- The concept of electric field was introduced to explain the force exerted on a charge by another charge, even when the second charge is removed.
Electric Field
- Electric field (E) is defined as the force experienced by a unit positive charge placed at a point in space, without disturbing the original positions of the source charges.
- The electric field produced by a point charge Q at a point r is given by E = (1/4πε₀) * Q/r², where r is the distance from the charge Q.
- The electric field is a vector quantity that varies with position and is dependent on the source charge.
- The force F on a charge q due to a charge Q is given by F = qE, where E is the electric field.
- The electric field E due to a point charge Q is independent of the test charge q.
Properties of Electric Field
- The electric field due to a point charge is radially outward for a positive charge and radially inward for a negative charge.
- The magnitude of the electric field depends only on the distance r from the charge Q.
- The electric field has a spherical symmetry, meaning it is the same at all points equidistant from the charge Q.
Electric Field due to a System of Charges
- The electric field E at a point r due to a system of charges q1, q2, ..., qn is the vector sum of the electric fields due to each individual charge.
- E = E1 + E2 + ... + En, where E1, E2, ..., En are the electric fields due to each charge.
Physical Significance of Electric Field
- The electric field is a convenient way to characterize the electrical environment of a system of charges.
- The electric field is independent of the test charge and is a characteristic of the system of charges.
- The concept of electric field is essential in time-dependent electromagnetic phenomena, where it can transport energy and has an independent dynamics.
Electric Field Lines
- Electric field lines are a pictorial representation of the electric field, with each line representing the direction of the electric field.
- The density of field lines represents the magnitude of the electric field, with a higher density indicating a stronger field.
- The field lines are continuous and can be drawn in any region, but the number of lines is not important.
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Description
Learn about the basics of electric charges and fields, including spark and crackle phenomena, lightning, and electric shocks.
