3. A \"test\" particle mass m is placed a distance I? away from an innitely long, straight wire of uniform lineal mass density A. The wire is xed in place. They interact through Newton's law of gravitation, with gravitational constant G. (a) The magnitude F of the gravitational force on the particle, due to the wire, must assume the general form F = E GaAmeEd, where g is a dimensionless constant, and a, b, c, and d are rational powers. Using dimensional analysis and known facts about gravitation, but without performing any integrals, determine the various powers in this scaling relation. (b) Find an integral expression for the force on the particle due to the long wire. Make sure to specify any coordinate system that you introduce. HINT: use a superposition principle. (0) Evaluate the integral, and infer the value of (S by comparing your exact answer to the form deduced in in part (a)