An interesting property of a conductor in static equilibrium is that extra charges on the conductor end up on its outer surface, regardless of where they originate. Consider a hollow metallic conductor with a uniform surface charge density. Since the conductor itself is in electrostatic equilibrium, there should not be any electric field inside the conductor. Now, assume a Gaussian surface enclosing the hollow portion. Applying Gauss's law, the inner surface of the hollow conductor will not...

The Earth is a good conductor of electricity, and it is so big that it can be considered an infinite source or sink of charges. It can easily exchange charges with any matter.
Generally, conductors like metals do not allow any excess charge to be present on them. Any excess charge added to metals easily flows away, for example, when a metal is placed on the Earth. This process is called earthing.
However, conductors can be charged by a process called induction. For example, consider charging a...

In the case of stringed instruments like the guitar, the elastic property that determines the speed of the sound produced is its linear mass density or the mass per unit length. This is simply called the linear density. If the string's linear density is constant along the string, then the linear density is simply the total mass divided by the total length.
The string's wave speed can be regulated by varying the linear density. Tension is the other property that determines the speed of...

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.

A coaxial cable consists of a central copper conductor used for transmitting signals, followed by an insulator shield, a metallic braided mesh that prevents signal interference, and a plastic layer that encases the entire assembly.
In the simplest form, a coaxial cable can be represented by two long hollow concentric cylinders in which the current flows in opposite directions. The magnetic field inside and outside the coaxial cable is determined by using Ampère's law. The magnetic field inside...

Flexible cables are commonly used in various applications for support and load transmission. Consider a cable fixed at two points and subjected to multiple vertically concentrated loads. Determine the shape of the cable and the tension in each portion of the cable, given the horizontal distances between the loads and supports.