Moving Charges and Magnetism
Class 12 · Physics
4 ideas in Class 12 Physics, explained in plain words, with games and quizzes to practise.
Magnetic Force and Motion in a Field
Part of: Magnetic Force and Circular Motion
A charge moving in a magnetic field feels a sideways force proportional to charge, speed, field and the sine of the angle between motion and field. Because the force stays perpendicular to motion, it bends the path into a circle without changing speed, Gyratory motion in machines like the cyclotron uses exactly this.
Why it matters. Mass spectrometers, cyclotrons and TV-era tubes all steer charges this way. Forgetting that magnetic force never speeds a charge up leads to wrong energy claims.
Formulas
- Magnetic force: F = q v B sin(theta)
- Circle radius: r = m v / (q B)
- Cyclotron frequency: f = q B / (2 pi m)
Key words
- Lorentz force
- : Combined electric and magnetic force on a moving charge.
- Cyclotron frequency
- : Circling rate of a charge in a field, fixed by charge, mass and field strength.
- Pitch
- : Forward distance covered in one turn of a helical path.
- Tesla
- : SI unit of magnetic field, equal to one newton per ampere-metre.
Try it in two minutes
- Multiply charge, speed and field, then multiply by sine of the entry angle.
- Point fingers along motion, curl toward field, read the thumb for force.
- Set the magnetic force equal to mass times v squared over r for the radius.
Try at home. Predict the path when a charge enters parallel, perpendicular and at a slant.
Biot-Savart Law and Circular Loop
Part of: Magnetic Force and Circular Motion
Every tiny current piece contributes a field that grows with current and length, weakens with squared distance, and depends on angle. Adding these gives the field of real shapes: circles around a straight wire and a strong axial field through a loop, largest at its centre.
Why it matters. Electromagnets, coils and motors are designed from these fields. Dropping the angle factor or using diameter for radius silently halves or doubles answers.
Formulas
- Biot-Savart: dB = (mu0/4pi) I dl sin(theta) / r^2
- Loop centre: B = mu0 N I / (2 R)
- mu0/(4 pi) = 10^-7 T m/A
Key words
- Biot-Savart law
- : Rule for the field of a small current piece based on current, length, angle and distance.
- Permeability
- : Constant mu nought setting the strength of magnetic effects of currents.
- Axial field
- : Magnetic field at points along the axis through a loop's centre.
Try it in two minutes
- Note current, length piece and angle for each part.
- Add contributions with direction by the right-hand rule.
- For a loop, use the centre formula and shrink with axial distance.
Try at home. Predict how stacking identical loops changes the centre field.
Ampere's Law and Forces Between Wires
Part of: Ampere's Law and Forces Between Wires
Ampere's law says the magnetic circulation around any loop equals mu nought times the enclosed current. It gives the wire field falling as 1 over distance, the uniform field inside a solenoid, and zero field outside an ideal toroid. Two parallel currents attract because each sits in the other's field.
Why it matters. Solenoids, toroids and the very definition of the ampere rest on this law. Mixing up inside and outside, or the attraction rule, breaks motor and meter reasoning.
Formulas
- Ampere: circulation of B = mu0 x enclosed I
- Straight wire: B = mu0 I / (2 pi r)
- Solenoid: B = mu0 n I; wire force per length = mu0 I1 I2 / (2 pi d)
Key words
- Ampere's law
- : Circulation of B around a loop equals mu nought times enclosed current.
- Solenoid
- : Long helical coil giving a nearly uniform field inside and weak field outside.
- Toroid
- : Solenoid bent into a ring, confining its field inside the ring.
- Ampere
- : Unit of current defined by the force between two parallel wires.
Try it in two minutes
- Draw an Amperian loop matching the symmetry.
- Set circulation equal to mu nought times enclosed current.
- For two wires, find one's field at the other and multiply by its current.
Try at home. Predict attraction or repulsion for two parallel wires with opposite currents.
Current Loop Torque and Galvanometer
Part of: Current Loop Torque and Galvanometer
A current loop in a field feels a torque proportional to turns, current, area, field and sine of angle, tending to face the field. The loop acts as a magnet of moment NIA. A moving-coil galvanometer balances this torque with a spring, and shunts or multipliers turn it into ammeters and voltmeters.
Why it matters. Motors spin on this torque and every analog meter is a converted galvanometer. Adding a shunt wrongly, or using a voltmeter in series, destroys readings.
Formulas
- Torque: T = N I A B sin(theta)
- Dipole moment: mu = N I A
- Shunt: S = Ig G / (I - Ig)
Key words
- Magnetic dipole moment
- : Turns times current times area, pointing along the loop's normal.
- Radial field
- : Field arranged to stay in the coil plane, giving uniform meter response.
- Shunt
- : Small parallel resistor that converts a galvanometer into an ammeter.
- Multiplier
- : Large series resistor that converts a galvanometer into a voltmeter.
Try it in two minutes
- Multiply turns, current and area for the dipole moment.
- Multiply by field and sine of angle for torque.
- Pick a tiny shunt for an ammeter and a large multiplier for a voltmeter.
Try at home. Predict which meter has lower resistance and why it must join in series.
What your child will practise
- Ampere's Law and Forces Between Wires: Space Quick Fire (Quick Fire)
- Biot-Savart Law and Circular Loop: Candy Puzzle (Clue Puzzle)
- Biot-Savart Law and Circular Loop: Ocean Quick Fire (Quick Fire)
- Current Loop Torque and Galvanometer: Jungle Quick Fire (Quick Fire)
- Magnetic Force and Motion in a Field: Space Puzzle (Clue Puzzle)
- Quiz: Ampere's Law and Forces Between Wires (8 questions)
- Quiz: Biot-Savart Law and Circular Loop (8 questions)
- Quiz: Current Loop Torque and Galvanometer (8 questions)
- Quiz: Magnetic Force and Motion in a Field (8 questions)