11.1.3 Faraday’s Law

• Faraday's Law connects the rate of change of flux linkage with induced e.m.f
• It is defined in words as:

The magnitude of the induced e.m.f is directly proportional to the rate of change of magnetic flux linkage

• Faraday's Law as an equation is defined as:

• Where:
  • ε = induced e.m.f (V)
  • Δ(Nɸ) = change in flux linkage (Wb turns)
  • Δt = time interval (s)

• If the interval of time becomes very small (i.e., in the limit of Δt → 0) the equation for Faraday's Law can be written as:

• Lenz’s law combined with Faraday’s law is given by the equation:  

• This equation shows:
  • When a bar magnet goes through a coil, an e.m.f is induced within the coil due to a change in magnetic flux
  • A current is also induced which means the coil now has its own magnetic field
  • The coil’s magnetic field acts in the opposite direction to the magnetic field of the bar magnet (shown by the minus sign)

• If a direct current (d.c) power supply is replaced with an alternating current  (a.c) supply, the e.m.f induced will also be alternating with the same frequency as the supply

Worked Example

Step 1: Write down the known quantities

• • Magnetic flux density, B = 80 mT = 80 × 10^-3 T
  • Area, A = 3.5 × 1.4 = (3.5 × 10^-2) × (1.4 × 10^-2) = 4.9 × 10^-4 m²
  • Number of turns, N = 350
  • Time interval, Δt = 0.18 s

 Step 2: Write out the equation for Faraday’s law:

Step 3: Write out the equation for the change in flux linkage:

• • The number of turns N and the coil area A stay constant
  • The flux through the coil changes as it rotates
  • Therefore, the change in flux linkage can be written as:

Δ(NΦ) = NA(ΔB)

Step 4: Determine the change in magnetic flux linkage

• • The initial flux through the coil is zero (flux lines are parallel to the coil face) 
  • The final flux through the coil is 80 mT (flux lines are perpendicular to the coil face)
  • This is because the coil begins horizontally in the field and is rotated 90°
  • Therefore, the change in flux linkage is:

Δ(NΦ) = NA(ΔB) = 350 × (4.9 × 10^-4) × (80 × 10^-3) = 0.014 Wb turns

Step 5: Substitute change in flux linkage and time into Faraday’s law equation:

= 0.076 V

Exam Tip