The induced emf in an inductor of inductance \(L\) varies with time according to \(\mathscr{E}_{\text {ind }}(t)=-2 C t\), where \(C\) is a positive constant.

(a) If there is no current through the inductor at \(t=0\), calculate the current as a function of time for \(t>0\).

(b) Is the current increasing or decreasing when \(t>0\) ?

(c) Discuss how your answer to part \(b\) is consistent with the sign of \(\mathscr{E}_{\text {ind }}\) and what you know about the behavior of inductors.