  In this paper, we present the Noether symmetries of locally rotationally
symmetric Bianchi type I (LRS BI), an anisotropic model, in the context of the
teleparallel gravity. We study a certain modified teleparallel theory based on
the action that, in particular, contains a coupling between the scalar field
and field strength (magnetism part). We derive the symmetry generators and show
that, by means of cyclic variables approach, we can not obtain a suitable
solution for field equations. Hence by the use of B.N.S. approach, we solve the
equations which carry Noether currents as well. By data analysis of the
obtained results, we show compatible results with observational data at the
last half the age of universe which is accelerating.
