Let's name the variables we're given and that we know:
Vrms: rms voltage; Vrms = 58.62 V
ΔImax: maximum (peak) current; ΔImax = 88.78 mA = 88.78*10^-3 A
f: frequency; f = 21.84 kHz = 21.84*10^3 Hz
Now let's name some unknowns:
Irms: rms current
XL: inductive reactance
L: inductance
From equations and variables we know:
Irms = ΔImax/sqrt(2) = 88.78*10^-3/sqrt(2)
Irms = 0.063 A
XL = Vrms/Irms = 58.62/0.063
XL = 930.476 Ω
Finally,
L = XL/(2πf) = 930.476/(2π*21.84*10^3)
L = 0.00678 H = 6.78 mH
