I have done an experiment named parallel action experiment, which shows the movement of a test coil in a magnetic field that is not allowed by Lorentz force law. Please see the video

The setup of this experiment is shown in Figure 1. The test coil carries a current that is influenced by the magnetic field B created by the magnet. The test coil, which is plane and perpendicular to its axle of rotation, can turn only in its plane. The video shows, when the current flows, signaled by the blinking of the led, the coil rotates in its plane.

Please read the article at
http://pengkuanem.blogspot.com/2013/03/blog-post.html
or
http://www.academia.edu/3116741/Theory_about_parallel_action_experiment

Does Lorentz force exert a force parallel to the current? NO. However, this experiment shows that, YES, it does exist a force parallel to the current. This experiment makes a plane coil turn in the magnetic field of a magnet. The axle crosses the plane of the coil perpendicularly in the center. Only force parallel to the current can make it turn.

First photography: Will this coil turn?
Second photography: The coil and the magnet.
Third photography: The led will turn on when current flows in the coil. The referential system of the setup.

Please see the video at
http://pengkuanem.blogspot.com/2013/03/lorentz-parallel-action-experiment.html