Electricity and magnetism are deeply connected. Current produces a magnetic field, and changes in a magnetic field produce current.
Basic Knowledge
Magnetic field (magnetic field, B): A field produced around magnets and electric currents. Unit: T (tesla).
Magnetic field lines: Closed curves that emerge from the N pole and enter the S pole
Current and magnetic fields:
・Magnetic field of a straight current: right-hand screw rule (the direction of rotation when a right-handed screw is advanced in the direction of the current is the direction of the magnetic field)
・Magnetic field of a solenoid (coil): Point the four fingers of the right hand in the winding direction; the thumb points toward the N pole
Force acting on a current in a magnetic field (Lorentz force):
F = BIL (B: magnetic field, I: current, L: length of conductor)
Direction: Fleming's left-hand rule (middle finger: current, index finger: magnetic field, thumb: force)
Electromagnetic induction: An electromotive force is produced when the magnetic flux through a coil changes (Faraday's law)
Lenz's law: The induced current flows in a direction that opposes the change in magnetic flux
Magnetic field (magnetic field, B)（a field around magnets and electric currents. Unit: T (tesla)）
Right-hand screw rule（the relationship between a straight current and the direction of the magnetic field around it）
Fleming's left-hand rule（a rule using the left hand to represent the directions of current, magnetic field, and force）
Electromagnetic induction（the phenomenon in which a change in magnetic flux produces an electromotive force. The principle of generators）
Lenz's law（the induced current flows in a direction that opposes the change in magnetic flux）
Magnetic flux (Φ)（the total amount of magnetic field passing through a coil. Φ = BS [Wb]）
Further Exploration (Background and Significance)
Distinguish Fleming's left-hand rule (electric motors) from the right-hand rule (generators). Left hand: current→force (motor); right hand: force→current (generator).
Faraday's law of electromagnetic induction: induced electromotive force ε = −ΔΦ/Δt (the rate of change of magnetic flux with time). The minus sign represents Lenz's law.
Transformers use electromagnetic induction. If the primary-coil voltage and number of turns are V₁ and N₁, and the secondary-coil voltage and number of turns are V₂ and N₂, then V₁/V₂ = N₁/N₂. By increasing voltage and decreasing current in transmission lines, Joule heat loss I²R can be reduced.
Applications of electromagnetic induction include IH cooking heaters (induction heating), contactless charging (smartphones), and MRI (magnetic resonance imaging), which are fundamental to modern technology.
- Right-hand screw rule: current→direction of the surrounding magnetic field
- Left hand: current×magnetic field → force (motor)
- Right hand: movement of conductor×magnetic field → induced current (generator)
- F = BIL
- Electromagnetic induction: change in magnetic flux → induced electromotive force
- Lenz's law: direction opposing the change
- Transformer: V₁/V₂ = N₁/N₂
Notes (Common Confusions)
① Distinguish the left hand (force received・motor) from the right hand (induced current・generator). ② According to Lenz's law, when magnetic flux increases, current flows in a direction that cancels it; when it decreases, current flows in a direction that compensates for it. ③ The important point in electromagnetic induction is the “change in magnetic flux.” If the magnetic field is constant, the induced electromotive force is zero. ④ In F = BIL, the force is greatest when B and I are perpendicular. If they are parallel, the force is zero.
Practice
- A conductor 0.1 m long carrying a current of 2 A is perpendicular to a magnetic field of 0.5 T. Find the force acting on it.
- Explain Lenz's law in terms of the relationship between the change in magnetic flux and the direction of induced current.
- A transformer has a primary side with 100 turns and 100 V, and a secondary side with 500 turns. Find the secondary voltage.