Electricity & Magnetism Formulas

Complete collection of electricity and magnetism formulas with detailed explanations, notation meanings, units, and real-world applications. Master electromagnetic phenomena.

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Electrostatics

Coulomb's Law

F = k\frac{q_1 q_2}{r^2}

The force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Notation:

F

:Electrostatic force

k

:Coulomb's constant

q_1, q_2

:Electric charges

r

:Distance between charges

Units:

F

:Newton (N)

k

:8.988 × 10⁹ N·m²/C²

q_1, q_2

:Coulomb (C)

r

:Meter (m)

Applications:

•Charged particle interactions
•Atomic structure
•Electrostatic attraction/repulsion

Limitations:

Point charges in vacuum

Electric Field

E = \frac{F}{q} = k\frac{Q}{r^2}

Electric field strength equals force per unit charge, or Coulomb's constant times charge divided by distance squared.

Notation:

E

:Electric field strength

F

:Force on test charge

q

:Test charge

k

:Coulomb's constant

Q

:Source charge

r

:Distance from source

Units:

E

:N/C or V/m

F

q

k

:N·m²/C²

Q

r

Applications:

•Capacitor design
•Particle accelerators
•Electrostatic shielding

Limitations:

Point charge or spherical symmetry

Electric Potential

V = k\frac{Q}{r}

Electric potential equals Coulomb's constant times charge divided by distance.

Notation:

V

:Electric potential

k

:Coulomb's constant

Q

:Source charge

r

:Distance from source

Units:

V

:Volt (V) = J/C

k

:N·m²/C²

Q

r

Applications:

•Voltage measurements
•Capacitor charging
•Electron energy levels

Limitations:

Point charge, zero potential at infinity

🔌

Current Electricity

Ohm's Law

V = IR

Voltage equals current times resistance.

Notation:

V

:Voltage (potential difference)

I

:Electric current

R

:Resistance

Units:

V

:Volt (V)

I

:Ampere (A)

R

:Ohm (Ω)

Applications:

•Circuit analysis
•Resistor calculations
•Voltage dividers

Limitations:

Ohmic materials only

Electric Power

P = VI = I^2R = \frac{V^2}{R}

Power equals voltage times current, or current squared times resistance, or voltage squared divided by resistance.

Notation:

P

:Electric power

V

:Voltage

I

:Current

R

:Resistance

Units:

P

:Watt (W) = J/s

V

I

R

:Ω

Applications:

•Power consumption
•Heating elements
•Electrical appliances

Limitations:

DC circuits or RMS values for AC

Resistance

R = \rho\frac{L}{A}

Resistance equals resistivity times length divided by cross-sectional area.

Notation:

R

:Resistance

\rho

:Resistivity

L

:Length

A

:Cross-sectional area

Units:

R

:Ω

\rho

:Ω·m

L

A

:m²

Applications:

•Wire resistance
•Resistor design
•Material characterization

Limitations:

Uniform material, constant temperature

🧲

Magnetism

Magnetic Force on Moving Charge

F = qvB\sin\theta

Magnetic force equals charge times velocity times magnetic field strength times sine of angle between velocity and field.

Notation:

F

:Magnetic force

q

:Electric charge

v

:Velocity

B

:Magnetic field strength

\theta

:Angle between v and B

Units:

F

q

v

:m/s

B

:Tesla (T)

\theta

:radians or degrees

Applications:

•Particle accelerators
•Mass spectrometers
•Magnetic confinement

Limitations:

Non-relativistic speeds

Magnetic Field due to Current

B = \frac{\mu_0 I}{2\pi r}

Magnetic field around a long straight wire equals permeability of free space times current divided by 2π times distance.

Notation:

B

:Magnetic field strength

\mu_0

:Permeability of free space

I

:Current

r

:Distance from wire

Units:

B

\mu_0

:4π × 10⁻⁷ T·m/A

I

r

Applications:

•Electromagnets
•Magnetic field measurement
•Current sensors

Limitations:

Long straight wire

Magnetic Flux

\Phi = BA\cos\theta

Magnetic flux equals magnetic field strength times area times cosine of angle between field and normal to area.

Notation:

\Phi

:Magnetic flux

B

:Magnetic field strength

A

:Area

\theta

:Angle between B and normal to A

Units:

\Phi

:Weber (Wb) = T·m²

B

A

:m²

\theta

:radians or degrees

Applications:

•Transformer design
•Induction motors
•Magnetic sensors

Limitations:

Uniform magnetic field

🔄

Electromagnetic Induction

Faraday's Law

\varepsilon = -\frac{d\Phi}{dt}

Induced electromotive force equals negative rate of change of magnetic flux.

Notation:

\varepsilon

:Induced EMF

\frac{d\Phi}{dt}

:Rate of change of magnetic flux

-

:Lenz's law sign

Units:

\varepsilon

\frac{d\Phi}{dt}

:Wb/s

Applications:

•Electric generators
•Transformers
•Induction heating

Limitations:

Single loop or coil

Self-Inductance

L = \frac{N\Phi}{I}

Self-inductance equals number of turns times magnetic flux divided by current.

Notation:

L

:Self-inductance

N

:Number of turns

\Phi

:Magnetic flux

I

:Current

Units:

L

:Henry (H) = Wb/A

N

:dimensionless

\Phi

:Wb

I

Applications:

•Inductor design
•Energy storage
•Filter circuits

Limitations:

Linear magnetic material

Mutual Inductance

M = \frac{N_2\Phi_{21}}{I_1}

Mutual inductance equals number of turns in second coil times flux through second coil due to current in first coil.

Notation:

M

:Mutual inductance

N_2

:Number of turns in second coil

\Phi_{21}

:Flux through second coil due to first coil

I_1

:Current in first coil

Units:

M

N_2

:dimensionless

\Phi_{21}

:Wb

I_1

Applications:

•Transformers
•Inductive coupling
•Wireless power transfer

Limitations:

Linear magnetic material

🌊

AC Circuits

RMS Values

V_{\text{rms}} = \frac{V_0}{\sqrt{2}}, I_{\text{rms}} = \frac{I_0}{\sqrt{2}}

Root mean square values equal peak values divided by square root of 2.

Notation:

V_{\text{rms}}

:RMS voltage

I_{\text{rms}}

:RMS current

V_0

:Peak voltage

I_0

:Peak current

Units:

V_{\text{rms}}, V_0

I_{\text{rms}}, I_0

Applications:

•AC power calculations
•Voltage measurements
•Power ratings

Limitations:

Sinusoidal waveforms

Impedance

Z = \sqrt{R^2 + (X_L - X_C)^2}

Impedance equals square root of resistance squared plus reactance difference squared.

Notation:

Z

:Impedance

R

:Resistance

X_L

:Inductive reactance

X_C

:Capacitive reactance

Units:

Z, R, X_L, X_C

:Ω

Applications:

•AC circuit analysis
•Filter design
•Impedance matching

Limitations:

Linear circuit elements

Resonance Frequency

f_0 = \frac{1}{2\pi\sqrt{LC}}

Resonance frequency equals one divided by 2π times square root of inductance times capacitance.

Notation:

f_0

:Resonance frequency

L

:Inductance

C

:Capacitance

Units:

f_0

:Hz

L

C

:Farad (F)

Applications:

•Tuned circuits
•Radio receivers
•Oscillators

Limitations:

Series or parallel resonance

Practice Problems

📝Calculate force between 2μC and -3μC charges 5cm apart
📝Find current in 10Ω resistor with 5V across it
📝Calculate magnetic force on 2C charge moving at 10m/s in 0.5T field

Try Interactive Calculators

Ohm's Law Coulomb's Law Electric Field Capacitance Capacitor Energy Wheatstone Bridge Impedance RMS Voltage Lorentz Force

Study Tips

💡Remember direction matters for vectors
💡Use right-hand rule for magnetic fields
💡Check units carefully in calculations