Physics - Electricity and Magnetism - Fundamentals

31 concise fundamentals covering electric fields, charged particles, magnetism, induction and transformers.

Charge | What are charge and conventional current?

Charge q is measured in coulombs (C). Like charges repel and unlike charges attract. Conventional current points in the direction positive charge would move; electrons in a wire move the opposite way.

Electric fields | What does an electric field tell you?

Force per unit positive charge: E = F/q, in N/C. A positive charge feels force along the field; a negative charge feels force opposite it.

Electric fields | What does Coulomb's law say?

The force magnitude between point charges is F = k|q₁q₂|/r², where k = 1/(4πε₀). Doubling distance quarters the force. Each charge feels an equal and opposite force.

Electric fields | How do fields from several charges combine?

Add the field vectors at the point. For one point charge, E = k|Q|/r², directed away from positive Q and towards negative Q. Add components, not just magnitudes.

Electric fields | How do you read field-line diagrams?

Arrows show force direction on a positive test charge. Closer lines mean a stronger field. Lines never cross. Between large opposite plates they are roughly straight and evenly spaced; near edges they curve.

Conductors | What happens to charge on a conductor at electrostatic equilibrium?

Excess charge rests on the surface and the field inside the conducting material is zero. A hollow cavity also has zero field if it contains no charge. The outside field meets the surface at right angles.

Conductors | Why are fields strongest near sharp points?

Surface charge is more concentrated there, making the nearby field stronger. A strong enough field can ionise air and allow charge to leak away.

Potential | What does potential difference mean?

Energy transferred per coulomb, measured in volts: 1 V = 1 J/C. Electric potential energy changes by ΔU = qΔV; work done by the electric field is −ΔU.

Potential | How do voltage and field relate between parallel plates?

For a uniform field, E = |ΔV|/d. Greater voltage or a smaller separation produces a stronger field. The field points from higher to lower potential.

Electric motion | How does a charged particle accelerate in a uniform field?

F = qE, so a = qE/m as vectors. Acceleration is constant if E is constant. Reverse the charge sign and the acceleration reverses.

Electric motion | How much kinetic energy can a voltage give a particle?

If other forces are negligible, the kinetic-energy gain equals the loss of electric potential energy. Through an accelerating voltage of magnitude V, ΔK = |q|V. For low speeds use K = ½mv².

Electric motion | Why can an electric field produce a parabolic path?

A particle entering across a uniform field keeps constant velocity perpendicular to the field and accelerates along the electric force. This is like projectile motion, with electric acceleration instead of gravity.

Magnetism | What produces a magnetic field?

Moving charges, including electric currents, produce magnetic fields. Field direction is the direction a compass north pole points. Field strength B is measured in tesla (T).

Magnetism | How do you find the field around a straight wire?

Point your right thumb along conventional current; curled fingers show the circular field direction. B = μ₀I/(2πr): more current strengthens it, greater distance weakens it.

Magnetism | What does a solenoid's field look like?

A solenoid is a coil of wire. Its field resembles a bar magnet's and is approximately uniform inside a long coil. Curl right-hand fingers along conventional current; the thumb points to its north end.

Magnetic force | When does a magnetic field exert force on a charge?

For a moving charge, F = |q|vB sinθ, where θ is between velocity and field. Force is zero for a stationary charge or parallel motion, and greatest for perpendicular motion.

Magnetic force | How do you find the direction of magnetic force?

For positive charge use the direction of v × B: point right-hand fingers along velocity and curl towards B; thumb gives force. Reverse for negative charge. Force is perpendicular to both v and B.

Magnetic force | What is the force on a current-carrying wire?

F = BIl sinθ, where θ is between current and field. Use conventional-current direction for the right-hand rule. Reverse the current or field to reverse the force.

Magnetic motion | Why does a magnetic field change direction but not speed?

The magnetic force is perpendicular to velocity, so it does no work. It changes momentum direction without changing kinetic energy. Perpendicular entry into a uniform field produces a circle.

Magnetic motion | What sets the radius of a charged particle's circular path?

r = mv/(|q|B), for perpendicular motion at non-relativistic speed. Greater mass or speed makes a larger circle; greater charge magnitude or field makes a smaller one.

Cyclotrons | What do the electric and magnetic fields do?

The electric field accelerates particles across the gap between the dees. The magnetic field bends them into semicircles inside the dees, without increasing their kinetic energy there.

Cyclotrons | Why must the gap voltage alternate?

Particles cross the gap in opposite directions on successive crossings, so the electric field must reverse to keep accelerating them. At non-relativistic speeds, T = 2πm/(|q|B) is independent of speed; the voltage frequency matches 1/T.

Cyclotrons | What sets the final energy of an ion?

At exit radius r, K = q²B²r²/(2m) for non-relativistic motion. For given ions, field and radius set the final energy. Gap voltage affects energy gained per crossing and the number of crossings needed.

Induction | What is magnetic flux?

A measure of magnetic field passing through an area: Φ = BA cosθ, where θ is between B and the area's normal. It is greatest when the field goes straight through, and zero when parallel to the surface. Unit: weber (Wb).

Induction | What is an induced emf?

A voltage produced by changing magnetic flux through a circuit. Emf is energy supplied per coulomb. An induced current flows only if there is a conducting path.

Induction | What does Faraday's law say?

The emf magnitude is N|ΔΦ/Δt| for N identical loops. More turns or a faster flux change gives a larger emf. Flux can change by changing field strength, area or orientation.

Induction | What does Lenz's law say?

Induced current creates a magnetic field that opposes the change in flux causing it. It opposes the change, not necessarily the original field. This prevents energy being created for free.

Induction | What are eddy currents?

Circulating induced currents inside a bulk conductor exposed to changing flux. They cause heating and can create magnetic braking. Slots or insulated laminations restrict their paths and reduce them.

Generators | How does a generator produce electricity?

Relative motion between a coil and magnetic field changes the coil's flux, inducing emf. A rotating coil produces alternating emf as its orientation changes. Mechanical energy supplies the electrical energy.

Transformers | How does a transformer change voltage?

Alternating current in the primary creates changing core flux, inducing secondary emf. Vₛ/Vₚ = Nₛ/Nₚ. More secondary turns steps voltage up; fewer steps it down. Steady DC does not give continuous induction.

Transformers | Why use high voltage to transmit power?

For the same power P = VI, higher voltage means lower current. Cable heating I²R is then smaller. An ideal transformer conserves power, so stepping voltage up steps current down.