Magnetism Formula Table
Reference for Magnetic Forces, Fields, and Induction equations.
Magnetic Forces
Force on Moving Charge
F = qvB sin(θ)Force F on charge q moving at velocity v in field B.
Force on Wire
F = BIL sin(θ)Force on wire length L carrying current I.
Radius of Circular Path
r = mv / qBRadius of motion for charge moving perp. to B-field.
Magnetic Fields (Sources)
Field near Straight Wire
B = (μ₀ · I) / (2πr)Field at distance r from infinite wire.
Field in Solenoid
B = μ₀ · n · IField inside coil. n = turns per unit length (N/L).
Biot-Savart Law
dB = (μ₀ I dl sinθ) / 4πr²Fundamental law for field created by current element.
Flux & Induction
Magnetic Flux
Φ = B · A · cos(θ)Field lines passing through Area A.
Faraday's Law
ε = -N · ΔΦ / ΔtInduced EMF (ε) opposes change in flux (Lenz Law).
Transformer Equation
Vp/Vs = Np/Ns = Is/IpVoltage/Current transformation ratio.
The Invisible Force directly.
From the compass involved in your pocket to the fusion reactors of the future, Magnetism is the invisible glue of the universe. It creates motion from electricity and electricity from motion.
The Quantum Origin
We usually see magnets as distinct from electricity, but they are deeply connected. Magnetism is purely a quantum mechanical effect.
Electron Spin
Every electron acts like a tiny bar magnet. In most stuff, they pair up (Up/Down) and cancel out. In Iron, they don't cancel—they align.
Moving Charges
When electrons *move* (current), they create a circular magnetic field around the wire. This is how we make Electromagnets.
The Right Hand Rule
The most famous "cheat code" in Physics. Use it to find the direction of the invisible force.
*Strictly for Positive charges. For Electrons, use Left Hand.
Deep Dive: The Equations
The force is maximized when the charge moves perpendicular (90°) to the field.
The field inside a long coil is uniform and strong. It depends on turn density ($n$) and current ($I$).
Frequently Asked Questions
What determines the strength of an electromagnet?
Three main factors determine the strength of a solenoid (electromagnet): 1) Current (I): More current means a stronger field. 2) Turns (N): More loops of wire concentrate the field. 3) Core Material: Inserting an Iron core can multiply the field strength by 1000x compared to air. The formula is $B = \mu n I$.
Why does a moving charge feel a force in a magnetic field?
This is the Lorentz Force. A magnetic field is essentially a relativistic side-effect of electricity. When a charge moves, its electric field distorts due to relativity, creating what we perceive as a 'magnetic' force. If the charge acts parallel to the field, no distortion happens (Force = 0). If it moves perpendicular, the effect is maximum.
What is the Right Hand Rule?
The Right Hand Rule is a visual trick to find the direction of magnetic forces. Point your Fingers in the direction of velocity (v). Curl them towards the Field (B). Your Thumb points to the Force (F). Note: This applies to positive charges. For electrons, use your Left Hand!
What is the difference between Magnetic Flux and Field?
Think of rain falling through a hoop. The Field (B) is how hard it complicates is raining (density of drops). The Flux (Φ) is the total amount of water passing through the hoop. If you tilt the hoop (change angle θ), less rain gets through, reducing Flux, even though the rain (Field) hasn't changed.
Why do magnets have North and South poles?
Magnetism arises from the 'spin' of electrons. In most materials, electrons spin in random directions, cancelling each other out. In magnets, they align. The 'North' pole is where the field lines exit, and 'South' is where they enter. You cannot have a North without a South because magnetic field lines must form closed loops.
Can a magnetic field do work on a particle?
No. This is a favorite trick question in physics exams. The magnetic force ($F_{mag}$) is always perpendicular to the velocity ($v$). Since Work = Force × Displacement × cos(θ), and the angle is always 90° (cos90 = 0), the work done is ZERO. Magnetic fields can change a particle's direction, but never its speed.
What is Tesla (T) vs. Gauss (G)?
Both function as units of Magnetic Field Strength. The Tesla (T) is the standard SI unit but is very large. The Gauss (G) is the CGS unit. 1 Tesla = 10,000 Gauss. The Earth's magnetic field is roughly 0.5 Gauss (0.00005 T), while an MRI machine is 1.5 to 3 Tesla.
How does an MRI machine work?
MRI (Magnetic Resonance Imaging) uses a massive superconducting magnet to align the protons (hydrogen atoms) in your body. It then blasts them with radio waves, knocking them out of alignment. As they snap back into place, they emit signals that computers turn into detailed 3D images of your soft tissues.
what is Induction?
Induction is the process of generating electricity using magnetism. Faraday's Law states that a changing magnetic flux creates a Voltage. This is how almost all power plants work: they spin a magnet inside a coil of wire (or vice versa), constantly changing the flux and pushing electrons to create current.
Why is Iron magnetic but Copper is not?
It comes down to atomic structure. Iron has 4 unpaired electrons in its D-shell that can easily align with neighbors to form 'Magnetic Domains'. Copper has a full D-shell with paired electrons (one spin-up, one spin-down), which cancels out their magnetic moments completely.