Answer
It takes more energy to increase the current from $10~mA$ to $20~mA$ than to increase the current from $0~mA$ to $10~mA$.
Work Step by Step
We can write an expression for the energy stored in an inductor:
$U = \frac{1}{2}~L~I^2$
Let $U_1 = \frac{1}{2}~L~I_1^2$ be the energy required to increase the current from $0~mA$ to $10~mA$. We can find the energy stored in the inductor when the current is $20~mA$:
$U_2 = \frac{1}{2}~L~I_2^2$
$U_2 = \frac{1}{2}~L~(2~I_1)^2$
$U_2 = 4\times \frac{1}{2}~L~I_1^2$
$U_2 = 4\times U_1$
We would need to provide energy in the amount of $4U_1-U_1 = 3U_1$ to increase the current from $10~mA$ to $20~mA$. Therefore, it takes more energy to increase the current from $10~mA$ to $20~mA$ than to increase the current from $0~mA$ to $10~mA$.
