Electric Charges And Fields Notes for NEET by Physics Wallah

Electric Charges and Fields is a foundational chapter in NEET Physics, covering concepts that are essential for solving electrostatics problems. Questions on Coulomb’s law, superposition, electric dipoles, electric flux, and Gauss’s law require a clear understanding of formulas, vector directions, and charge distributions. Practising numerical problems alongside concept revision can help you avoid common mistakes and apply these principles accurately.

To strengthen these concepts, you should combine textbook revision with regular practice and assessments. Physics Wallah supports NEET preparation through dedicated courses for Class 11, Class 12, and droppers, with live and recorded classes, handwritten notes, Daily Practice Problems (DPPs), mock tests, previous years’ questions (PYQs), and regular assessments.

Electric Charge: Definition And Field Production

Electric charge is a property of matter that produces an electromagnetic field in the surrounding region. A charge placed in this field experiences a force.

The state of motion of a charge determines the associated physical effects:

Electric charge is a scalar quantity. Its SI unit is coulomb (C), and its CGS unit is statcoulomb or esu.

Important conversions include:

• 1 C = 3 × 10^9 esu

• 1 faraday = 96500 C

A neutral atom has equal numbers of protons and electrons. Ordinary charging occurs through the transfer of electrons, not protons.

• Addition of electrons produces negative charge.

• Removal of electrons produces positive charge.

• Like charges repel.

• Unlike charges attract.

• Charge does not depend on the speed of a body.

Quantisation and Conservation Of Charge

Electric charge is quantised, meaning that the net charge on an isolated body is an integral multiple of the elementary charge.

Formula: q = ne

Where:

• q = net charge

• n = integer

• e = magnitude of the elementary charge

Elementary charge: e = 1.6 × 10⁻¹⁹ C

Electrons are transferred as complete particles during ordinary charging, so the net charge on a body is expressed as an integral multiple of (e).

Memory tip: The numerical value of charge in coulombs can be very small, but (n) in (q=ne) must be an integer for the net charge of an isolated body.

The law of conservation of charge states that the total charge of an isolated system remains constant. Charge is transferred between bodies or redistributed within a system, but the total charge is conserved.

Conductors, Insulators, And Charging Methods

Conductors contain mobile charge carriers that allow charge to move through the material. In electrostatic equilibrium, the electric field inside the conducting material is zero, and any excess charge on an isolated conductor resides on its surface.

Insulators have charges that are more tightly bound to their atoms or molecules, so charge movement through the material is restricted.

Three Methods of Charging

1. Charging by friction: When two suitable materials are rubbed together, electrons may transfer from one material to the other. The bodies acquire equal and opposite charges if the system is otherwise isolated.

2. Charging by conduction: A charged body touches another conducting body, allowing charge to flow between them. The final charge distribution depends on the conductors’ geometry and electrical conditions.

In conduction, a charged conductor is connected to another conductor. Charge flows until both conductors reach the same potential. For two spheres of radii R1 and R2, with initial charges q1 and q2:

q₁′/R₁ = q₂′/R₂

If their initial total charge is q₁ + q₂, the final charges are:

Final charge on sphere 1:

q₁′ = R₁(q₁ + q₂)/(R₁ + R₂)

Final charge on sphere 2:

q₂′ = R₂(q₁ + q₂)/(R₁ + R₂)

Equal-sized spheres share charge equally.

Induction causes charge redistribution without direct contact. A nearby charged body separates charges inside a neutral conductor. The conductor remains neutral unless grounding and separation steps are completed.

Coulomb’s Law

Coulomb’s law gives the magnitude of the electrostatic force between two stationary point charges separated by distance (r):

Coulomb’s law:

F = (1/4πε₀) × |q₁q₂|/r²

Alternatively:

F = k|q₁q₂|/r²

Where:

k = 1/(4πε₀) ≈ 9 × 10⁹ N m²/C²

Here, ε₀ is the permittivity of free space.

The force is:

• Repulsive for like charges.

• Attractive for unlike charges.

• Equal in magnitude and opposite in direction on the two charges.

• An inverse-square, central, conservative, and long-range force.

In a medium of dielectric constant K: Fmedium = Fair / K

If the separation also changes, both the medium and distance factors must be included.

Superposition Principle And Equilibrium

The superposition principle states that the force between any two charges is not changed by the presence of other charges. However, the net force is the vector sum of all individual forces:

Net force:

F⃗ net = F⃗ ₁ + F⃗ ₂ + F⃗ ₃ + ...

For electrostatic equilibrium under the forces being considered:

F⃗ net = 0

For two same-sign charges, the zero-force point lies between them and closer to the smaller charge. For opposite-sign charges, it lies outside the interval on the side of the smaller-magnitude charge.

In a symmetric polygon containing equal charges of the same sign at every corner, the net force and electric field at the centre are zero.

Electric Field And Electric Field Lines

Electric field is force per unit positive test charge: 

Electric field: E⃗ = F⃗ /q₀

For a point charge q, the electric field magnitude at distance r is: E = k|q|/r²

The field points outward from a positive charge and inward towards a negative charge.

The force on a charge placed in an electric field is: F⃗ = qE⃗

A positive charge experiences force along the field, while a negative charge experiences force opposite to it.

Properties of Electric Field Lines

• Field lines originate from positive charges and terminate on negative charges or extend to infinity.

• Electric field lines never intersect.

• The density of field lines indicates the relative strength of the field.

• Field lines are parallel and equally spaced in a uniform electric field.

• At the surface of a conductor in electrostatic equilibrium, the electric field just outside is perpendicular to the surface.

• The electric field inside the conducting material is zero in electrostatic equilibrium.

Electric Field Due To Important Charge Distributions

Symmetry simplifies electric field calculations for common charge distributions. The following formulas are useful for conceptual and numerical questions in NEET Physics.

Uniformly Charged Ring

For a ring of radius R carrying total charge Q, the electric field at an axial point a distance x from its centre is:

E = kQx/(R² + x²)^(3/2)

At the centre, x = 0, so: E = 0

The magnitude of the axial field is maximum at: |x| = R/√2

At distances much greater than the ring’s radius, the field approaches that of a point charge with total charge Q.

Infinite Line Charge

For an infinitely long straight line with uniform linear charge density λ, the electric field magnitude at perpendicular distance r is: E = |λ|/(2πε₀r)

Alternatively: E = 2k|λ|/r

The field is directed radially outward for positive λ and inward for negative λ.

Infinite Plane Sheet

For an infinite, uniformly charged nonconducting sheet with surface charge density σ: E = |σ|/(2ε₀)

The field magnitude is independent of the distance from the sheet.

For the surface of an ideal conductor in electrostatic equilibrium, the electric field just outside is: E = |σ|/ε₀

Here, σ is the local surface charge density, and the electric field inside the conducting material is zero.

Spherical Charge Distributions

For a thin, uniformly charged conducting spherical shell of radius R and total charge Q:

Inside the shell (r < R): E = 0

Outside the shell (r ≥ R): E = k|Q|/r²

For a uniformly charged nonconducting solid sphere of radius R and total charge Q:

Inside the sphere (r < R): E = k|Q|r/R³

Outside the sphere (r ≥ R): E = k|Q|/r²

The field inside a uniformly charged nonconducting sphere increases linearly with distance from the centre. By contrast, the field inside the material of a conducting spherical shell is zero in electrostatic equilibrium, provided there is no charge inside its cavity.

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance. If the separation between the charges is d, the magnitude of the dipole moment is: p = qd

The electric dipole moment is directed from the negative charge towards the positive charge.

For a short dipole at a point far away compared with the separation between its charges:

Electric field on the axial line: E axial = 2kp/r³

Electric field on the equatorial line: E equatorial = kp/r³

At the same distance, the axial field magnitude is twice the equatorial field magnitude. The equatorial field points opposite to the dipole moment.

A dipole placed in a uniform electric field experiences torque: τ = pE sin θ

Here, θ is the angle between the dipole moment and the electric field. An ideal dipole in a uniform electric field experiences zero net force, although it can experience a torque.

Electric Flux and Gauss’s Law

Electric flux measures the electric field passing through a surface. For a uniform electric field through a flat surface:

Φ = EA cos θ

Here, θ is the angle between the electric field and the area vector, which is perpendicular to the surface.

• When the field is parallel to the area vector, Φ = EA.

• When the field is parallel to the surface, Φ = 0.

• For a closed surface, the flux contribution is positive where the field exits and negative where it enters.

Gauss’s law states that the net electric flux through a closed surface equals the enclosed charge divided by the permittivity of free space.

∮ E⃗ · dA⃗ = Q enclosed/ε₀

The net flux depends on the total charge enclosed by the surface. External charges can produce an electric field on the surface, but their net contribution to the total flux through a closed surface is zero.

Gauss’s law is particularly useful for calculating fields when the charge distribution has spherical, cylindrical, or planar symmetry.

Electric Flux Through a Cube

For a point charge q at the centre of a cube, the flux through each of its six faces is: Φ per face = q/(6ε₀)

For a point charge q at a corner of a cube, the total flux through the original cube is: Φ through cube = q/(8ε₀)

The flux through each of the three faces opposite the corner containing the charge is: Φ per opposite face = q/(24ε₀)

These results follow from symmetry and assume an ideal point charge at the stated position.

Electric Charges and Fields builds the foundation for electrostatics and requires a clear understanding of charge properties, Coulomb’s law, electric fields, dipoles, flux, Gauss’s law, and charged-particle motion. Memorising formulas alone is not sufficient; you also need to understand their conditions of application and practise numerical questions involving vectors and symmetry. Physics Wallah supports NEET preparation through dedicated courses for Class 11, Class 12, and droppers, along with live and recorded classes, handwritten notes, DPPs, mock tests, PYQs, and regular assessments.

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