Answer
$V_L = 0$
Work Step by Step
In part (j), we found that $V_2 = 10~V$
Let's consider a clockwise loop around the outside loop of the circuit. We can use the loop rule to find $V_L$:
$\mathscr{E}+V_L -V_2 = 0$
$10~V+V_L-10~V = 0$
$V_L = 0$