7.9.4 Faraday's & Lenz's Laws

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

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

• Lenz’s Law gives the direction of the induced e.m.f as defined by Faraday’s law:

The induced e.m.f acts in such a direction to produce effects that oppose the change causing it

Experimental Evidence for Lenz’s Law

• To verify Lenz’s law, the only apparatus needed is:
  • A bar magnet
  • A coil of wire
  • A sensitive ammeter

• Note: a cell is not required
• A known pole (either north or south) of the bar magnet is pushed into the coil, which induces a magnetic field in the coil
  • Using the right-hand grip rule, the curled fingers indicate the direction of the current and the thumb indicates the direction of the induced magnetic field

• The direction of the current is observed on the ammeter
  • Reversing the magnet direction would give an opposite deflection on the meter

• The induced field (in the coil) repels the bar magnet
• This is because of Lenz’s law:
  • The direction of the induced field in the coil pushes against the change creating it, ie. the bar magnet

Lenz’s law can be verified using a coil connected in series with a sensitive ammeter and a bar magnet

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

• Where:
  • ε = induced e.m.f (V)
  • N = number of turns of coil
  • Δɸ = change in magnetic flux (Wb)
  • Δt = time interval (s)

• This equation shows that the gradient of a magnetic flux against time graph is the e.m.f

• 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

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
  • Angle between coil and field lines = 40^o
    • Therefore θ, the angle between the normal to the area and the field lines = (90 − 40) = 50°

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

Step 3: Write out the equation for flux linkage:

Step 4: Substitute values into flux linkage equation:

ΦN = (80 × 10^-3) × (4.9 × 10^-4) × 350 × cos(50) = 8.82 × 10⁻³ Wb turns

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