When a loop rotating in a uniform magnetic field.
The magnetic flux is changing which will induce electric field along the loop (produce voltage).
If the loop is rotating with constant angular velocity $\omega$ . (The angle is $\omega t$)
The magnetic flux in the loop will be $\Psi =\int \vec{B}\cdot d\vec{A}= B A cos(\omega t)$
So the induced emf $ = -\frac {d\Psi}{dt}=B A \omega sin(\omega t)$

The following simulation show how it works dynamically.
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So a loop rotating in a uniform magnetic field will generate electric power.
Reverse the process, a current in the uniform magnetic field will rotate (it become a motor).
Please check out [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=912.0]Current Loop in magnetic field (How motor works!)[/url]