IB DP Physics: HL复习笔记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:Problems Involving Faraday’s Law

• 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

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:

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