Electric Charges and Fields

• The video aims to comprehensively cover electric charges and fields in one session.
• The session is structured into four parts: Charges and Coulomb's Law, Field and Application, Dipole and Flux, and Gauss's Law and Application.
• Approximately 100 questions are included.
• Students should remain focused and avoid repetitive break requests.
• Questions include board-level subjective questions converted to objective formats, along with NEET, AIIMS, and JIPMER level questions.

Defining Charge

• Charge is an intrinsic property of matter that causes attraction or repulsion.
• Like charges repel each other, unlike charges attract.
• A neutral body contains an equal amount of positive and negative charge, resulting in no net charge.
• Only electrons can be transferred between objects.
• A neutral body becomes negatively charged by gaining electrons and positively charged by losing them.

Current, Charge, and Units

• Current is the rate of flow of electrons.
• The unit of current is the ampere, and the unit of time is the second.
• Electrical charge can be expressed as current multiplied by time.
• The standard international unit of charge is the coulomb (C), defined as Ampere * Second.
• 1 Coulomb is equivalent to 3 * 10^9 electrostatic units (ESU) or Franklin.
• 1 electromagnetic unit (EMU) equals 10 Coulombs.

Properties of Charge

• Charge is a scalar quantity.
• Charge is quantized, existing in discrete units that are integral multiples of the elementary charge (e).
• The smallest unit of charge is the charge of an electron: e = 1.6 * 10^-19 Coulombs.
• Charge is always associated with mass; a body gains mass when acquiring electrons and loses mass when losing them.
• Charge is invariant of speed.
• Charge is conserved; the total charge in an isolated system remains constant.
• Charge can neither be created nor destroyed but can only be transferred.

Charge and Motion

• A charge at rest produces an electric field.
• A charge moving with constant velocity produces both electric and magnetic fields.
• An accelerating charge radiates electromagnetic waves.

Charging Methods

• Three methods of charging: friction, conduction, and induction.
• Friction involves rubbing two objects, causing electron transfer and resulting in opposite charges.
• Conduction involves direct contact, allowing charge transfer until objects reach the same potential; for identical objects, charge is equally distributed.
• Induction involves bringing a charged object near a neutral one, causing charge separation; grounding allows charge flow, resulting in a net charge.

Quarks as Fundamental Particles

• Protons and neutrons are composed of quarks, and are not fundamental particles.
• Protons consist of two up quarks and one down quark.
• Neutrons consist of two down quarks and one up quark.
• Up quarks have a charge of +2/3 e, while down quarks have a charge of -1/3 e.
• Quarks are not found in an isolated state due to being highly unstable outside of protons and neutrons.

Coulomb's Law

• Describes the force between two charges: F = k * q1 * q2 / r^2
• k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them.
• k is also expressed as 1 / (4 * pi * epsilon_0), where epsilon_0 is the permittivity of free space.
• Epsilon_0 has a value of 8.85 * 10^-12 C^2 / (N*m^2).
• The force between two point charges acts along the line joining them.

Vector Form of Coulomb's Law

• The force on charge 2 due to charge 1 is given by F21 = k * q1 * q2 / r^3 * r21.
• r21 is the position vector of charge 2 with respect to charge 1 (r2 - r1).

Superposition Principle

• The net force on a charge due to multiple charges is the vector sum of forces from each individual charge.
• For an isolated system, charge lost by one body equals charge gained by another.
• Coulomb's Law is valid only for point charges.
• Equal and opposite forces of equal magnitude act on charges according to Coulomb's Law.

Properties of Electrostatic Force

• The electrostatic force is a conservative force.
• The work done in moving a point charge in a closed path is zero.

Electric Field

• The region around a charge in which it can exert force.
• Mathematically, electric field is force per unit positive test charge: E = F/q.
• Its unit is Newtons per Coulomb (N/C).
• Electric field is a vector quantity and follows the superposition principle, adding up individual vector components.
• Electric field due to a point charge: E = k*q/r^2.
• Electric fields point outward from positive charges and inward towards negative charges.
• Electric field lines originate from positive charges and terminate at negative charges and cannot intersect.
• Where electric field lines are denser, the electric field E is high, and vice versa.

Properties of Electric Field Lines in Conductors

• Electric field lines are perpendicular to the surface and do not form closed loops.

Charge Distributions

• Linear Charge Distribution: Charge per unit length, λ = Q/L (Unit: Coulomb per meter).
• Surface Charge Distribution: Charge per unit area, σ = Q/A (Unit: Coulomb per meter squared).
• Volume Charge Distribution: Charge per unit volume, ρ = Q/V (Unit: Coulomb per meter cubed).

Electric Dipole

• Combination of positive and negative charges separated by a distance.
• The electric dipole moment is a vector quantity, pointing from negative to positive.
• It is given by p = q * d, where q is the charge and d is the separation distance.
• Units of dipole moment: Coulombs * Meter.
• A dipole in an electric field experiences torque given by τ = p x E = pE sin(θ), where θ is the angle between the dipole moment and the electric field vectors.

Different Placements of a Dipole

• A dipole in external motion starting with charges at rest will have an electric field only.
• Electric field to the axis of two charges on either side involves components solved using trigonometry.
• General equations with vector calculus should be used with angle Theta for net results.
• In General: E Net varies along these results and is inversely proportional to r cubed.
• Electric field is proportional over P 2K P/ R where p is the dipole movement equal where to equal q, P is 2 k q.

Short Dipole Definition

• Short dipole variations include axial and equilateral variations.
• Direction and vector components due to both fields change the actual value overall.
• Electric field varies inversely with R cubed for the point.
• An electric dipole must be kept in the axial field along with a large distance along the line.

Flux

• The number of field lines crossing a given amount of area.
• The stronger the amount or field of electric strength, the larger the flux.
• Area which an electric current is traveling.
• Three dependent components: Electric Field, Area, and Orientation.
• The area is normal to the surface.
• The SI unit of Electric Flux equals Newton Meters Square.
• Number of fields are proportional to area and length and derivation components.
• Gauss's law is essentially Coulomb's law and relates electric flux through a closed surface to the enclosed charge.
• The formula for electric flux through a closed surface is: Flux = Integral of E dot dA.
• The total net flux through any surface is also equal to: Flux = Q enclosed / Epsilon Not.
• Charges outside the enclosed surface do not contribute to the total flux through it.
• Flux is independent of the shape of the enclosed Gaussian surface, and only depends on the enclosed charge.
• The location of charges within the Gaussian surface doesn't affect the total flux.
• Electric field intensity at a Gaussian surface is due to all charges present, both inside and outside the surface.
• Incoming flux is considered negative and outgoing flux is considered positive in a closed surface.
• Zero net flux does not necessarily mean the electric field is zero.
• Zero electric field inside the Gaussian surface implies zero net flux.
• Net flux is 0 when closed surface is placed in an uniform electric field because the incoming flux is equivalent to the outgoing flux.
• When a charge Q is enclosed by a spherical Gaussian surface of radius R, doubling the radius does not change the outward electric flux.
• The electric field is due to every charge, while the net q is only due to the enclosed charge.
• The electric field inside a charged shell is zero due to no enclosed charge.
• Electric flux through a closed surface in an external electric field is zero, unless there is charge inside.
• When a charge is placed at the center of the sphere, Flux = q / epsilon not.

Flux and Symmetry

• A charge at the corner of a cube contributes 1/8 of its flux through the cube, given by q / 8 * epsilon not.
• A charge placed at the edge of a cube affects 4 cubes.
• A charge at the center of a cube emits flux through all six surfaces equally.

Applications of Gauss's Law: Electric Field Due to a Shell

• Electric field inside a charged shell is zero.
• Electric field outside the shell at a distance x from the center: E = kQ/x^2, where k is Coulomb's constant.
• Electric field on the surface of the shell: E = kQ/R^2, where R is the radius.
• The Electric field vs Radius graph for a shell starts at 0, going to a maximum at the surface and then gradually decreasing
• A conducting spherical shell will be at 0 field inside the shell, and then decrease squared as it goes out

Electric Field Due to a Solid Sphere

• The electric field formula for a point in the center of a solid sphere differs from outside it.
• e field should be calculated, calculating how much charge is on the certain surface with unit multiplier.
• Volume of v has change m.
• Ratios can be used to calculate the field.
• General formula: Q times smallRadiusCubed / bigRadiusCubed.
• E in = k * q *r / R cubed.
• A solid Sphere the electric-field in is directly proportionate to r.
• At surface this is = keq / r^2.
• Oustide the Solid sphere it has to be keq = X^2.

Electric Field Due to an Infinite Charged Wire

• A cylindrical Gaussian surface is used for an infinite charged wire.
• Electric field lines are radial from the wire.
• Flux is calculated using three sides.
• The electric field because of is calculated using flux1 + flux2 + flux3.
• Use integral of e times DA = qa / epsilon.
• General Formula e = 2k lambda / r, which is inverse proportional to R.
• The electric field because of the other sides equals 0, where the net flux is 0

Electric Field Due to a Thin Sheet

• Areas are measured to measure the electric field through a thin sheet.
• E *a = q / epsilon * 0.
• QA = sigman = surface charge density.
• The Electric Field is outward.
• Final equation: sigman / 2 epsilon 0.
• The value does not depend on location and remains constant.

Flux

• Flux is independent of the shape and size of the surface and the charge located outside the surface.

Conducting vs. Non-Conducting Surfaces (Solid)

• Graphs behave differently inside and outside.
• Inside a non-conducting solid surface, the graph is proportional, with a different behavior outside.

Infinitely Long Sheet

• The infinitely long sheet's graph is noteworthy and extends in opposite directions.
• The expression for the electric field is important.
• Electric field is maximum at plus/minus R/2.

Conducting Cylinder

• A conducting cylinder behaves like a thin charged wire when viewed from the outside.
• Electric field for a conducting cylinder: 2kλ/r (where k is a constant and λ is the linear charge density).

Mechanical Pressure

• Direct formula for pressure: σ²/2ε₀ (where σ is surface charge density and ε₀ is the permittivity of free space).
• Electric field: σ/ε₀

Homework

• Complete all questions from the session and all derivations.

Leaderboard

• Arka, Shweta, Ankit.
• Jatin, Ruby, Shubham.
• Shahzad, Divyanshu, Pankaj.
• Sumit, Aarti, Jayant.
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• Mohit.

Key Takeaways

• Approximately 182 slides were covered.
• Approximately 100 questions were completed.
• Electric Charges and Fields was covered in approximately 4.5 hours.
• Focus on the included notes as well as NCERT definitions for examination preparation.