QUIZ 1

Electric Field

The electric field (E) at any point is defined as the electrostatic force (F) exerted on a positive test charge (q₀) placed there:[E = F/q₀].

Electric Field Lines

Visual representations of electric fields that indicate direction and magnitude; their density shows the field's strength.

Gauss’ Law

Relates the net electric flux (Φ) through a closed surface to the net charge (q_enc) enclosed by that surface:[ε₀Φ = q_enc].

Electric Flux

The amount of electric field piercing a surface, defined as [dΦ = E · dA] for an area element and [Φ = ∫E · dA] for total flux.

Spherical Symmetry

For a point outside a spherical shell of charge (q):[E = (1/4πε₀)(q/r²)]; inside the shell, the electric field is zero.

Cylindrical Symmetry

For an infinitely long line of charge with linear charge density (λ):[E = λ/(2πε₀r)], where r is the distance from the line.

Planar Symmetry

For an infinite nonconducting sheet with surface charge density (σ):[E = σ/(2ε₀)]; for two parallel conducting plates, [E = σ/ε₀].

Conductors

Excess charge on an isolated conductor resides on its surface; the electric field inside is zero, and just outside, it is perpendicular to the surface:[E = σ/ε₀].

Field of a Point Charge

The electric field (E) due to a point charge (q) at distance (r) is given by [E = (1/4πε₀)(q/r²)hat{r}].

Superposition Principle

The net electric field from multiple charges is the vector sum of the fields due to each charge.

Dipole Definition

A dipole consists of two equal and opposite charges separated by a distance (d).

Field on the Dipole Axis

The electric field along the axis of a dipole is [E = (1/2πε₀)(qd/z³)], where qd is the dipole moment and z is the distance from the dipole center.

Linear Charge Density

For a line of charge with uniform linear charge density (λ), the electric field at distance (r) is [E = λ/(2πε₀r)].

Surface Charge Density

For a disk with uniform surface charge density (σ), the electric field at a point on the axis is [E = (σ/(2ε₀))(1 - z/√(z² + R²))].

Force on a Charge

A charge (q) in an external electric field (E) experiences a force [F = qE].

Torque on a Dipole

A dipole in an electric field experiences a torque [τ = p × E], where p is the dipole moment.

Potential Energy of a Dipole

The potential energy of a dipole in an electric field is [U = -p · E].

Electric Flux Definition

The electric flux (Φ) through a surface is the amount of electric field piercing it, given by [Φ = E · A] for a uniform field.

Closed Surface Flux

For a closed surface, the net flux is [Φ = ∮E · dA].

Charge Distribution in Conductors

Excess charge on an isolated conductor resides on its surface, and the electric field inside is zero in electrostatic equilibrium.