Comparison of Key Electromagnetic & Newtonian Laws - Compiled By BILRED

 

Comparison of Key Electromagnetic & Newtonian Laws

Law/Effect	Formula/Equation	Key Variables & Meaning	What It Describes/Applies To	Similarities/Differences
Coulomb’s Law (Electric Force)	${\displaystyle F=k\frac{q_1{q}_2}{r^2}}$	- $F$: Electric force (N) - $k$: Coulomb constant $9\times {10}^9$ Nm²/C² - $q_1,q_2$: Charges (C) - $r$: Distance (m)	Describes the force between two point charges. Similar to Newton’s gravitational law but for electrostatics.	Inverse Square Law: Like gravity but for electric charges.
Electric Field ($E$)	${\displaystyle E=\frac{F}{q}=k\frac{Q}{r^2}}$	- $E$: Electric field (N/C) - $Q$: Source charge (C) - $r$: Distance (m)	Defines the field created by a charge and the force it exerts on another charge.	Like gravitational field ($g$), but for electric forces.
Gauss’s Law (Electric Fields)	${\displaystyle \oint \mathbf{E}\cdot d\mathbf{A}=\frac{Q_{\text{enc}}}{{\epsilon }_0}}$	- $\mathbf{E}$: Electric field (N/C) - $dA$: Surface area element (m²) - $Q_{\text{enc}}$: Enclosed charge (C)	Relates the total electric flux through a closed surface to the charge inside. Used for symmetrical charge distributions.	Similar to Ampère’s Law, but for electric fields instead of magnetic fields.
Electric Potential ($V$)	${\displaystyle V=k\frac{Q}{r}}$	- $V$: Electric potential (V) - $Q$: Charge (C) - $r$: Distance (m)	Defines electric potential at a point due to a charge. Related to work done by moving a charge in an electric field.	Like gravitational potential energy but for charges.
Ampère’s Law (Magnetic Fields)	${\displaystyle \oint \mathbf{B}\cdot d\mathbf{s}={\mu }_0{I}_{\text{enc}}}$	- $B$: Magnetic field (T) - $d\mathbf{s}$: Path element (m) - $I_{\text{enc}}$: Enclosed current (A)	Relates the circulation of the magnetic field around a closed loop to the enclosed current. Used in solenoids and toroids.	Similar to Gauss’s Law but for magnetic fields.
Magnetic Force (Lorentz Force)	${\displaystyle F=q(\mathbf{E}+\mathbf{v}\times \mathbf{B})}$	- $F$: Force on charge (N) - $q$: Charge (C) - $\mathbf{E}$: Electric field (N/C) - $\mathbf{B}$: Magnetic field (T) - $\mathbf{v}$: Velocity (m/s)	Describes the force on a moving charge in electric and magnetic fields. Used in motors, particle physics, and railguns.	Combines electric and magnetic forces.
Hall Effect	${\displaystyle V_H=\frac{BId}{net}}$	- $V_H$: Hall voltage (V) - $B$: Magnetic field (T) - $I$: Current (A) - $d$: Width of conductor (m) (the distance across which the Hall voltage is measured) - $n$: Charge carrier density - $e$: Elementary charge -t thickness of conductor in direction of magnetic field	The formation of a voltage across a conductor due to a perpendicular magnetic field. Used in Hall sensors and  material studies.	Uses Lorentz force but in a different way (across a conductor).
Biot-Savart Law	${\displaystyle d\mathbf{B}=\frac{{\mu }_0}{4\pi }\frac{Id\mathbf{l}\times \mathbf{r}}{r^3}}$	- $d\mathbf{B}$: Small magnetic field (T) - $d\mathbf{l}$: Small current element (m) - $r$: Distance from element (m)	Describes the magnetic field created by a small current element. Used to calculate fields in wires and loops.	More detailed than Ampère’s Law but harder to apply.
Faraday’s Law (Induction)	${\displaystyle \mathcal{E}=-\frac{d{\mathrm{\Phi }}_B}{dt}}$	- $\mathcal{E}$: Induced EMF (V) - ${\mathrm{\Phi }}_B$: Magnetic flux (T·m²)	Explains how a changing magnetic flux induces voltage in a conductor. Used in generators and transformers.	Key to electromagnetic induction (motors, generators).
Lenz’s Law	"Induced current opposes the change in flux"	- Same as Faraday’s Law	Determines the direction of induced current.	Explains the negative sign in Faraday’s Law.
Newton’s Second Law	${\displaystyle F=ma}$	- $F$: Force (N) - $m$: Mass (kg) - $a$: Acceleration (m/s²)	Fundamental law of motion. Used in dynamics, including railguns.	Base equation for all motion.
Third Equation of Motion	${\displaystyle v^2=u^2+2as}$	- $v$: Final velocity (m/s) - $u$: Initial velocity (m/s) - $a$: Acceleration (m/s²) - $s$: Displacement (m)	Describes motion under constant acceleration. Used in railgun exit velocity calculations.	Derived from Newton’s laws.
Railgun Exit Velocity	${\displaystyle v=\sqrt{2aL}}$	- $a$: Acceleration (m/s²) - $L$: Rail length (m)	Determines how fast a projectile exits a railgun.	Directly derived from Newton’s Second Law and Lorentz force.

Key Takeaways:

✔ Gauss’s Law vs. Ampère’s Law: Both relate a field (E or B) to its source (charge or current) via an integral.
✔ Lorentz Force vs. Hall Effect: Both involve the force on charges in a magnetic field, but Hall Effect applies to conductors, while Lorentz Force applies to moving particles.
✔ Newton’s Laws & Motion Equations: Essential for understanding forces acting on objects (including railguns!).
✔ Faraday’s Law vs. Lenz’s Law: Faraday’s Law explains how EMF is induced, while Lenz’s Law tells us the direction of the induced current.

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