Electric Charges & Fields - Chapter 1

Flashcards for Electric Charges & Fields - Chapter 1

Key derivations in Chapter 1

Electric field due to Point Charge, Dipole (Axial & Equatorial), Torque on a dipole, Gauss's law, Infinitely Long Wire, Infinitely Plane Sheet, Charged Spherical Shell

Electric field at a point on the axis of an electric dipole

Etotal = kq [ (r+a)^2 - (r-a)^2 ] / (r^2-a^2)^2

Key derivations in Chapter 1

Electric field due to Point Charge, Dipole (Axial & Equatorial), Torque on a dipole, Gauss's law, Infinitely Long Wire, Infinitely Plane Sheet, Charged Spherical Shell

Electric field at a point on the axis of an electric dipole

Etotal = kq [ (r+a)^2 - (r-a)^2 ] / (r^2-a^2)^2

Simplified Electric field (axial) when a << r

Eaxial = k * 2p / r^3

Electric Field Intensity On The Equatorial Line Of An Electric Dipole

Equatorial = k * p / (r^2 + a^2)^(3/2)

Electric field (Equatorial) when a <<< r

E equatorial = kp / r^3

Torque on Electric Dipole in a Uniform Electric Field

Torque, Z = pEsinθ

Electric Flux

Electric flux is defined as the total number of electric field lines passing normal through the surface

Electric Flux Formula

Electric Flux, Φ = E · ds = ∫Eds cosθ

Gauss's Law

Gauss's law states that the total electric flux associated with any closed surface which encloses some charge q is equal to 1/ε₀ times the amount of charge enclosed.

Gauss's Law Formula

∮ E⋅ds = q/ε₀

Applications of Gauss's Law

Electric field intensity due to a charged spherical shell, Electric field intensity at a point near an infinitely long straight uniform charged wire, Electric field intensity at a point near an uniformly charged infinite thin plane sheet

Electric field due to an infinitely long uniformly charged wire

E = λ / (2πε₀r)

Definition of Linear Charge Density

λ = q/l (linear charge density)

Electric field due to a uniformly charged infinite plain sheet

E = σ / (2ε₀)

Definition of Surface Charge Density

σ = q/A (Surface charge density)

Electric field inside a uniformly charged thin spherical shell

E = 0

Electric field outside a uniformly charged thin spherical shell

E = q / (4πε₀r^2) = σR^2 / (ε₀r^2)