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Formula Induced Voltage along a Moving Rectangular Loop Magnetic field    Width    Velocity

Formula: Induced Voltage along a Moving Rectangular Loop

Induced Voltage

This induced voltage is generated along a rectangular very long conductor loop of width \( w \), which is moved into a homogeneous constant magnetic field \( \class{violet}{B} \) with velocity \( v \). In this way, the magnetic flux through the enclosed area of the conductor loop increases.

Magnetic field

A time-independent, homogeneous magnetic field into which the conductor loop is moved.


Width of the rectangular conductor loop. The width does not change.


Velocity of the conductor loop moving into the magnetic field \( \class{violet}{B} \).
  • If the velocity \( v \) is time independent, then the induction voltage \( U_{\text{ind}} \) is also time independent.
  • If the velocity \( v(t) \) is time dependent, then the induced voltage \( U_{\text{ind}}(t) \) also changes with time. This is the case, for example, when the conductor loop falls into the magnetic field under the influence of the gravitational force and thus its velocity increases.