The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop...

Biasing metal-semiconductor junctions involves applying a voltage across the junction. Specifically, the metal is connected to a voltage source, while the semiconductor is grounded. This technique is essential for controlling the direction and magnitude of current flow in electronic devices, including diodes, transistors, and photovoltaic cells.
In Schottky junctions, where the semiconductor is n-type, applying a positive voltage to the metal relative to the semiconductor reduces its Fermi...

An important concept in studying metabolism and energy is that of chemical equilibrium. Most chemical reactions are reversible. They can proceed in both directions, releasing energy into their environment in one direction, and absorbing it from the environment in the other direction. The same is true for the chemical reactions involved in cell metabolism, such as the breaking down and building up of proteins into and from individual amino acids, respectively. Reactants within a closed system...

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...

The German physicist Heinrich Hertz (1857–1894) was the first to generate and detect certain types of electromagnetic waves in the laboratory. Starting in 1887, he performed a series of experiments that confirmed the existence of electromagnetic waves and verified that they travel at the speed of light. Hertz used an alternating-current RLC (resistor-inductor-capacitor) circuit that resonated at a known frequency and connected it to a loop of wire. High voltages induced across the gap in...

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the loop can be calculated using the Biot-Savart law.