A \(1-\) H inductor carries \(10 \mathrm{A},\) and a \(10-\mathrm{H}\) inductor carries \(1 \mathrm{A}\). Which contains more stored energy?

Electromagnetism is a fundamental branch of physics that studies the relationship between electric currents and magnetic fields. This interaction is described by Maxwell's equations, which unify electricity, magnetism, and light.

An inductor, a basic component in electromagnetism, functions under these principles. When an electric current passes through an inductor, a magnetic field is generated around it. The strength of this field is related to the amount of current flowing and the physical characteristics of the inductor. This process is unavoidable in any circuit containing conductive materials and has practical applications in various electronic devices, from transformers to motors and sensors.

Inductance is the property of an electrical conductor by which a change in current through it induces an electromotive force (EMF) in both the conductor itself (self-inductance) and any nearby conductors (mutual inductance). The unit of inductance is the henry (H).

Inductors store energy in the magnetic field that is created by the electric current passing through them. The amount of inductance reflects the inductor's ability to store magnetic energy. A higher inductance implies a greater ability to store energy, assuming the current remains the same. Inductance is determined by factors like the number of turns in the coil, the cross-sectional area of the coil, the coil length, and the core material.

Energy storage in inductors is a key concept in electromagnetism. The energy is stored in the magnetic field generated by the current flowing through the coil of an inductor. The formula for calculating the energy stored in an inductor is given by: \[ W = 0.5 \cdot L \cdot I^2 \]where \(W\) is the stored energy in joules, \(L\) is the inductance in henrys, and \(I\) is the current in amperes passing through the inductor.

This relationship shows that the energy stored is proportional to the square of the current and directly proportional to the inductance, which highlights how changes in these quantities influence the inductor's energy storage capacity.

Physics problem solving involves understanding concepts, identifying relevant principles, applying equations, and performing calculated analysis. The process often consists of several steps: defining the problem, translating it into mathematical terms, calculating numerical solutions, and then interpreting those solutions.

In the given exercise, the problem involved comparing the stored energy between two inductors with different inductances and currents. It required the application of the energy storage formula for inductors. After performing calculations for each scenario, the energy values were directly compared to determine which inductor contained more stored energy. This systematic approach to solving physics problems is crucial for students to develop a deep understanding of the subject and enhance their analytical skills.