Faraday's Law Physics Example 5

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Example 5

hard
A square coil with 200 turns and side length 0.1 m0.1 \text{ m} is in a magnetic field that decreases uniformly from 0.5 T0.5 \text{ T} to 0 T0 \text{ T} in 0.2 s0.2 \text{ s}. Calculate the induced EMF. In which direction does the induced current flow (clockwise or anticlockwise, if the field points into the page)?

Solution

  1. 1
    Area: A=0.12=0.01 m2A = 0.1^2 = 0.01 \text{ m}^2. Change in flux per turn: ΔΦ=ΔB×A=(0−0.5)×0.01=−0.005 Wb\Delta\Phi = \Delta B \times A = (0 - 0.5) \times 0.01 = -0.005 \text{ Wb}.
  2. 2
    Induced EMF: ∣E∣=N∣ΔΦ∣Δt=200×0.0050.2=5 V|\mathcal{E}| = N\frac{|\Delta\Phi|}{\Delta t} = 200 \times \frac{0.005}{0.2} = 5 \text{ V}.
  3. 3
    By Lenz's law: the field is decreasing into the page, so the induced current opposes the change by creating its own field into the page → current flows clockwise (using the right-hand rule).

Answer

∣E∣=5 V, current flows clockwise|\mathcal{E}| = 5 \text{ V, current flows clockwise}
Faraday's law gives the magnitude of induced EMF; Lenz's law gives the direction. The induced current always opposes the change in flux — this is a consequence of energy conservation.

About Faraday's Law

The induced EMF in a circuit equals the negative rate of change of magnetic flux through the circuit.

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More Faraday's Law Examples

Example 1 medium

A coil with [formula] turns experiences a change in magnetic flux from [formula] to [formula] in [fo

Example 2 hard

A single loop of area [formula] is in a magnetic field that increases uniformly from [formula] to [f

Example 3 medium

A coil of [formula] turns has an area of [formula]. The magnetic field through it decreases from [fo

Example 4 medium

A coil of [formula] turns has a magnetic flux that changes from [formula] to [formula] in [formula].

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