Two sides of the loop are parallel to the x axis, and two sides are parallel to the y axis. The integration path is such that side 1 is traversed in the positive x direction, side 2 in the negative y direction, side 3 in the negative x direction, and side 4 in the positive y direction. Calculate the contribution to the circulation integral due to each segment of the loop, and determine the net current through the loop that must be present.

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)