Learn & Review: A Level Physics Revision: All of Electromagne

Electromagnetism Revision Summary

This summary covers the key concepts of electromagnetism, including magnetic fields, forces on current-carrying wires, magnetic flux, and electromagnetic induction through Faraday's Law and transformers.

1. Magnetic Fields

• Earth's Magnetic Field: The Earth acts like a large bar magnet with a North and South Pole.

• Magnetic Field Lines:

  • Always travel from North to South.
  • The direction indicates where a free North Pole would move.
  • Uniform Field: Represented by equally spaced and parallel lines.

• Magnetic Monopoles: Free North or South poles (magnetic monopoles) have not been observed.

• Magnetic Field Around a Current-Carrying Wire:

  • The field lines are concentric circles around the wire.
  • Notation:
    • A circle with a cross (X) indicates current going into the screen/page (like the back of an arrow).
    • A circle with a dot (•) indicates current coming out of the screen/page (like the front of an arrow).
  • Direction:
    • Current into the screen: Magnetic field is clockwise.
    • Current out of the screen: Magnetic field is anticlockwise.
  • Right-Hand Grip Rule:
    • Imagine gripping the wire with your right hand.
    • Your thumb points in the direction of the conventional current (positive to negative).
    • The curl of your fingers shows the direction of the magnetic field lines.
    • Crucial: Must use the right hand and consider conventional current.

• Magnetic Field Inside a Solenoid:

  • Can be assumed to be uniform.
  • The direction of the current determines the North and South poles of the solenoid.

2. Force on a Current-Carrying Wire in a Magnetic Field

• Condition: A current-carrying wire placed in an external magnetic field experiences a force.
• Formula: The magnitude of the force is given by: $F = BIL \sin \theta$
  • $F$: Force (Newtons)
  • $B$: Magnetic flux density (Teslas, T) - a measure of magnetic field strength.
  • $I$: Current (Amperes, A)
  • $L$: Length of the wire (meters, m)
  • $\theta$: Angle between the wire and the magnetic field.
• Key Points:
  • Maximum Force: Occurs when $\theta = 90^\circ$ (field perpendicular to the wire), as $\sin 90^\circ = 1$. The formula simplifies to $F = BIL$.
  • Zero Force: Occurs when $\theta = 0^\circ$ or $180^\circ$ (wire parallel to the field), as $\sin 0^\circ = \sin 180^\circ = 0$.
• Fleming's Left-Hand Rule: Used to determine the direction of the force.
  • Use your left hand.
  • Thumb: Direction of Force (motion).
  • First finger (Index finger): Direction of the Magnetic Field ($B$).
  • Second finger (Middle finger): Direction of the Conventional Current ($I$).
  • These three must be mutually perpendicular.

3. Charged Particles in a Magnetic Field

• Force on a Moving Charge: A charged particle moving in a magnetic field experiences a force.
• Formula: The magnetic force on a single charge is given by: $F = qvB$ (when the velocity is perpendicular to the field)
  • $q$: Charge (Coulombs, C)
  • $v$: Velocity of the charge (m/s)
  • $B$: Magnetic flux density (T)
• Circular Motion: If a charged particle enters a magnetic field perpendicular to its velocity, the magnetic force acts as a centripetal force, causing the particle to move in a circle.
  • $F_{magnetic} = F_{centripetal}$
  • $qvB = \frac{mv^2}{r}$
• Radius of Curvature: Rearranging the equation gives the radius of the circular path: $r = \frac{mv}{qB}$
  • $m$: Mass of the particle (kg)
  • $r$: Radius of the circular path (m)

4. Magnetic Flux ($\Phi$)

• Definition: The product of the magnetic flux density perpendicular to an area and the area itself.
• Formula: $\Phi = BA \cos \theta$
  • $\Phi$: Magnetic flux (Webers, Wb)
  • $B$: Magnetic flux density (T)
  • $A$: Area (m²)
  • $\theta$: The angle between the magnetic field lines and the normal (a line perpendicular) to the area.
• Key Points:
  • Maximum Flux: Occurs when the field lines are perpendicular to the area ($\theta = 0^\circ$, field parallel to the normal). $\cos 0^\circ = 1$, so $\Phi = BA$.
  • Zero Flux: Occurs when the field lines are parallel to the area ($\theta = 90^\circ$, field perpendicular to the normal). $\cos 90^\circ = 0$, so $\Phi = 0$.
• Units:
  • Magnetic Flux Density ($B$): Tesla (T)
  • Magnetic Flux ($\Phi$): Weber (Wb)
• Base Units:
  • $T = kg \cdot A^{-1} \cdot s^{-2}$
  • $Wb = kg \cdot m^2 \cdot A^{-1} \cdot s^{-2}$
• Magnetic Flux Linkage: For a coil with $N$ turns, it is $N\Phi$.

5. Faraday's Law of Electromagnetic Induction

• Discovery: Moving a magnet near a conductor (or changing the magnetic field) can induce an electromotive force (EMF) and hence a current. This is the principle behind generators.
• Law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linkage.
• Formula: $E = -\frac{\Delta(N\Phi)}{\Delta t}$
  • $E$: Induced EMF (Volts, V)
  • $N$: Number of turns in the coil
  • $\Phi$: Magnetic flux (Wb)
  • $\Delta t$: Change in time (seconds, s)
  • The formula can also be written as $E = -N \frac{\Delta B A \cos \theta}{\Delta t}$, considering changes in $B$, $A$, or $\theta$.
• Lenz's Law (The Minus Sign):
  • The direction of the induced current is such that it opposes the change producing it.
  • This is a consequence of the conservation of energy. For example, if a North pole approaches a coil, the induced current will create a North pole in the coil to repel the approaching magnet.

6. AC Generator

• Principle: A coil rotating in a magnetic field induces an alternating EMF (and current).
• Flux Linkage Variation: As the coil rotates, the angle $\theta$ between the normal to the coil and the magnetic field changes, causing the magnetic flux linkage ($N\Phi = NBA \cos \theta$) to vary sinusoidally with time.
• EMF Generation: According to Faraday's Law, the rate of change of this flux linkage induces an EMF. The gradient of the flux linkage vs. time graph represents the magnitude of the induced EMF.

7. Transformers

• Components: Consist of two coils (primary and secondary) wound around a soft iron core. The core provides an easy path for magnetic field lines.
• Operation:
  1. An AC voltage is applied to the primary coil.
  2. The AC current creates a continuously changing magnetic flux in the iron core.
  3. This changing flux passes through the secondary coil.
  4. By Faraday's Law, the changing flux induces an AC EMF in the secondary coil.
  5. There is no direct electrical connection between the coils; energy transfer is via the changing magnetic field.
• Voltage and Turns Ratio: $\frac{N_S}{N_P} = \frac{V_S}{V_P}$
  • $N_S$: Number of turns in the secondary coil.
  • $N_P$: Number of turns in the primary coil.
  • $V_S$: Voltage across the secondary coil.
  • $V_P$: Voltage across the primary coil.
• Current and Turns Ratio (Power Conservation): $\frac{V_S}{V_P} = \frac{I_P}{I_S}$
  • $I_S$: Current in the secondary coil.
  • $I_P$: Current in the primary coil.
  • This relationship arises because Power In ≈ Power Out ($V_P I_P \approx V_S I_S$).
• Types:
  • Step-up Transformer: $N_S > N_P$, so $V_S > V_P$ and $I_S < I_P$.
  • Step-down Transformer: $N_S < N_P$, so $V_S < V_P$ and $I_S > I_P$.