In a previous paper [Phys. Essays 5, 451 (1992)] we introduced a relativistic electromagnetic force law in a theory of relativity alternative to the Lorentz force law in special relativity, and demonstrated that no existing experimental evidence can convincingly distinguish between the two force laws. In addition, we proposed a ''uniform circular motion'' experimental test to distinguish between the two force laws. In the present paper we first emphasize important distinctions between the two force laws. Next, we propose a ''linear motion'' experimental test for the two force laws which is complementary to the previously proposed test. The experimental test proposed here is less expensive and more practical to carry out than the previously proposed test.