Physics Formulas

Physics Formulas for Electromagnetism

Coulomb’s Law		Q = electric charge r₂₁ = distance from Q₁ to Q₂ k = 8.99 x 10⁹ N m²/C²
Permittivity of free space ε₀		ε₀ = 8.85 x 10^-12 C²/N m²
Electric Field		where is the force experienced by a test charge q
Electric Field of a point charge Q₁
Superposition of electric fields from many point charges
Electric flux Φ_E through a closed surface		element of surface area directed normal to the surface
Gauss’ Law		1^st Maxwell Equation
Uniform charge distributions for filaments, surfaces, and volumes		where λ is the linear charge density, σ is the surface charge density, and ρ is the volume charge density
Acceleration of a charged particle of mass m and charge q in an electric field
Dipole moment p of an electric dipole		where the length is directed from –Q to +Q
Torque on an electric dipole in an electric field
Work to move a test charge q from r₁ to r₂ in the electric field of a point charge Q

Potential energy of a test charge q in the presence of a point charge Q
Work to move a test charge q from P₁ to P₂ in an arbitrary electric field
Change in potential energy to move a test charge q from P₁ to P₂ in an arbitrary electric field
Electric potential difference
Electric potential at r of a point charge Q referenced from ∞
Electric potential at P of a system of N point charges
Potential energy of an arbitrary system of point charges Q_i
Electric potential at a perpendicular distance a from an infinite, uniformly charged wire with a linear charge density λ		r₀ is the reference distance where V(r₀) = 0
Electric field of a conducting surface with charge density σ
Electric current I
Ohm’s Law
Ohmic loss or Joule heating
Current density		where A is the cross-sectional area, n_e is the free electron density, is the electron drift velocity, τ is the mean time between collisions, m_e is the mass of the electron and σ is the conductivity
Conductivity σ
Resistivity ρ
Ohm’s Law
Resistance of a wire of cross-sectional area A and length ℓ
Temperature dependence of resistivity for most conductors		where ρ₀ is the resistivity at a reference temperature T₀ and α is the temperature coefficient
Resistors in series
Resistors in parallel
Kirchhoff’s junction rule
Kirchhoff’s loop rule
Capacitance C
Capacitance C of a parallel plate capacitor of surface area A, plate separation d, and dielectric constant κ
Stored energy U in a capacitor
Capacitors in parallel
Capacitors in series
Dielectric constant κ		where E_a is the applied electric field and E is the net electric field
Energy density in an electric field
Magnetic force law
Biot-Savart law		where N/A²is the permeability of free-space, r is the displacement from dℓ to P and I is the current in the direction of dℓ
Magnetic induction on the axis of a current I in a circular loop of radius a		determine using the right hand rule
Magnetic dipole moment of a current loop		m is a vector with direction given by the right hand rule, A is the cross-sectional area
Gauss’s Law for Magnetic Fields		2^nd Maxwell Equation
Ampère’s Law
Magnetic induction from a current I in a long straight wire		r is the perpendicular distance from the wire
Magnetic induction in a solenoid		where n is the number of turns/unit length and is along the axis of the solenoid as given by the right hand rule
Motion perpendicular to a uniform magnetic field B		where m, v, and q are respectively the mass, speed, and charge of the particle, r_L is the Larmor radius, and ω_C is the cyclotron frequency
Lorentz force law
Force on a current-carrying wire
Torque on a current loop in a magnetic field B		where m is the magnetic moment of the current loop
Faraday’s Law (the – sign in the last two terms is the result of Lenz’s law)		3^rd Maxwell Equation
Induced electromotive force
Electromotive force of a generator rotating at an angular speed ω		where N is the number of turns in the generator coil, B is the uniform magnetic induction across the coil and A is the cross-sectional area of the coil
Torque of a simple electric motor		where N is the number of turns in the motor coil, B is the uniform magnetic induction across the coil, A is the cross-sectional area of the coil, I is the current and θ is the angle between the normal of the coil and the magnetic induction
Electromotive force driving a simple electric motor		where r is the resistance of the motor and the other symbols are as above
Displacement current I_d
Ampère-Maxwell Law		4^th Maxwell Equation
RC Circuit (discharging)		where τ_C is the time constant
RC Circuit (charging)
Self-Inductance L
Self-Inductance of a Solenoid		where N is the number of turns, ℓ the length, n the number of turns per unit length and A the cross-sectional area of the solenoid
Energy stored in an Inductor
Energy density in a magnetic field
Energy density in an electromagnetic field
Mutual Inductance M		where 1 refers to one circuit and 2 to another conjoined only by mutual inductance
Relationship of electromotive force to the number of turns N in a transformer		where s refers to the secondary coil and p to the primary coil
LR Circuit (decaying)		where τ_L is the time constant
LR Circuit (increasing)
LC Circuit
LRC Circuit
Alternating Current Circuits

ε0 = 8.85 x 10-12 C2/N m2

where is the force experienced by a test charge q

element of surface area directed normal to the surface

1st Maxwell Equation

where λ is the linear charge density, σ is the surface charge density, and ρ is the volume charge density

where the length is directed from –Q to +Q

r0 is the reference distance where V(r0) = 0

where A is the cross-sectional area, ne is the free electron density, is the electron drift velocity, τ is the mean time between collisions, me is the mass of the electron and σ is the conductivity

where ρ0 is the resistivity at a reference temperature T0 and α is the temperature coefficient

where Ea is the applied electric field and E is the net electric field

where N/A2 is the permeability of free-space, r is the displacement from dℓ to P and I is the current in the direction of dℓ

determine using the right hand rule

m is a vector with direction given by the right hand rule, A is the cross-sectional area

2nd Maxwell Equation

r is the perpendicular distance from the wire

where n is the number of turns/unit length and is along the axis of the solenoid as given by the right hand rule

where m, v, and q are respectively the mass, speed, and charge of the particle, rL is the Larmor radius, and ωC is the cyclotron frequency

where m is the magnetic moment of the current loop

3rd Maxwell Equation

where N is the number of turns in the generator coil, B is the uniform magnetic induction across the coil and A is the cross-sectional area of the coil

where N is the number of turns in the motor coil, B is the uniform magnetic induction across the coil, A is the cross-sectional area of the coil, I is the current and θ is the angle between the normal of the coil and the magnetic induction

where r is the resistance of the motor and the other symbols are as above

4th Maxwell Equation

where τC is the time constant

where N is the number of turns, ℓ the length, n the number of turns per unit length and A the cross-sectional area of the solenoid

where 1 refers to one circuit and 2 to another conjoined only by mutual inductance

where s refers to the secondary coil and p to the primary coil

where τL is the time constant

ε₀ = 8.85 x 10^-12 C²/N m²

1^st Maxwell Equation

r₀ is the reference distance where V(r₀) = 0

where A is the cross-sectional area, n_e is the free electron density, is the electron drift velocity, τ is the mean time between collisions, m_e is the mass of the electron and σ is the conductivity

where ρ₀ is the resistivity at a reference temperature T₀ and α is the temperature coefficient

where E_a is the applied electric field and E is the net electric field

where N/A²is the permeability of free-space, r is the displacement from dℓ to P and I is the current in the direction of dℓ

2^nd Maxwell Equation

where m, v, and q are respectively the mass, speed, and charge of the particle, r_L is the Larmor radius, and ω_C is the cyclotron frequency

3^rd Maxwell Equation

4^th Maxwell Equation

where τ_C is the time constant

where τ_L is the time constant