# Induced voltage in an arc of wire

We know that time varying magnetic field produces voltage in a coil. But what if the wire forms a semicircle or an arc instead of a complete loop, will such magnetic field produce voltage between the ends of the wire? If yes, what is the formula to calculate the induced voltage?

Yes, it induces the voltage across the both ends, but no current can flow. This is similar to motion of conductor inside a magnetic filed, or motional EMF. The motional EMF is described as: $$\oint ( \vec{v}^{\,}\times \vec{B}^{\,})d \vec{l}^{\,}$$ Here $\vec{v}^{\,}$ is the speed, $\vec{B}^{\,}$ is the magnetic field, and the integral should be evaluated along the conductor curve. This situation is not exactly a time varying magnetic filed, but everything here is relative if you know what i mean. The best example is antenna. The equation doesn't provide an immediate quantitive values to your question, i try here to make it clear that the EMF can be induced in an open loop circuit.