An important distinction exists between the electric field induced by a changing magnetic field and the electrostatic field produced by a fixed charge distribution. Specifically, the induced electric field is nonconservative because it does not work in moving a charge over a closed path. In contrast, the electrostatic field is conservative and does no net work over a closed path. Hence, electric potential can be associated with the electrostatic field but not the induced field. The following...

The fact that emfs are induced in circuits implies that work is being done on the conduction electrons in the wires. What can possibly be the source of this work? We know that it’s neither a battery nor a magnetic field, as a battery does not have to be present in a circuit where current is induced, and magnetic fields never do any work on moving charges. The source of the work is in fact an electric field that is induced in the wires. For example, if a stationary conductor is placed in a...

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 the...

Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the magnetic field at a point "P2", midway between the wires. Also, evaluate the magnetic field when the direction of the current is reversed in the second wire.

When a conductor is placed in an external electric field, the free charges in the conductor redistribute and very quickly reach electrostatic equilibrium. The resulting charge distribution and its electric field have many interesting properties, which can be investigated with the help of Gauss's law.
Suppose a piece of metal is placed near a positive charge. The free electrons in the metal are attracted to the external positive charge and migrate freely toward that region. This region then has...

Gauss' law relates the electric flux through a closed surface to the net charge enclosed by that surface. Gauss's law can be applied to find the electric field and the charge enclosed in a region depending on its charge distribution.
Consider a cross-section of a thin, infinite conducting plate having a positive charge. For such a large thin plate, as the thickness of the plate tends to zero, the positive charges lie on the plate's two large faces. Without an external electric field, the...