The magnetic potential energy stored in a certain inductor is $25\ \text{mJ}$, when the current in the inductor is $50\ \text{mA}$. This inductor is of inductance
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Always ensure units are converted to standard SI units (Joules for energy, Amperes for current) before substituting into the formula to avoid power-of-ten errors.
Step 1: What we are looking for. We have a coil (an inductor) that stores some magnetic energy when current flows through it. We know the stored energy and the current, and we want to find the inductance $L$.
Step 2: The idea behind it. An inductor stores energy in its magnetic field. The energy depends on how big the current is and on the inductance. The handy formula is $U = \frac{1}{2} L I^2$.
Step 3: Make the units friendly. Energy $U = 25$ mJ $= 0.025$ J. Current $I = 50$ mA $= 0.05$ A. Working in plain SI units keeps the answer clean.
Step 4: Turn the formula around. We want $L$, so we rearrange to get $L = \dfrac{2U}{I^2}$.
Step 5: Put the numbers in. First square the current: $I^2 = (0.05)^2 = 0.0025$. Then $L = \dfrac{2 \times 0.025}{0.0025} = \dfrac{0.05}{0.0025}$.
Step 6: Finish the division. $\dfrac{0.05}{0.0025} = 20$. So the inductance is $20$ H. That matches option (D). \[ \boxed{L = 20\ \text{H}} \]