Faraday's Law Physics Example 2

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Example 2

hard
A single loop of area 0.04 m20.04 \text{ m}^2 is in a magnetic field that increases uniformly from 00 to 0.6 T0.6 \text{ T} in 0.3 s0.3 \text{ s}. What is the induced EMF?

Solution

  1. 1
    Change in flux: ΔΦ=Bf⋅A−Bi⋅A=(0.6−0)(0.04)=0.024 Wb\Delta \Phi = B_f \cdot A - B_i \cdot A = (0.6 - 0)(0.04) = 0.024 \text{ Wb}.
  2. 2
    With N=1N = 1: E=−NΔΦΔt=−1×0.0240.3=−0.08 V\mathcal{E} = -N\frac{\Delta \Phi}{\Delta t} = -1 \times \frac{0.024}{0.3} = -0.08 \text{ V}
  3. 3
    Magnitude: ∣E∣=0.08 V=80 mV|\mathcal{E}| = 0.08 \text{ V} = 80 \text{ mV}.

Answer

∣E∣=80 mV|\mathcal{E}| = 80 \text{ mV}
Magnetic flux is the product of the magnetic field and the area it passes through. A changing field through a loop induces an EMF, even if the loop itself does not move.

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 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].

Example 5 hard

A square coil with 200 turns and side length [formula] is in a magnetic field that decreases uniform

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