Understanding how an object moves along a path requires distinguishing between motion over a time span and motion at a precise moment. A useful example is a vehicle traveling along a straight and level path, where its position at any given time is known. The initial step in analyzing this motion is to measure how far the vehicle travels over a fixed time period. This measurement, called average velocity, is computed by dividing the total change in position by the duration over which the change...

Polymers are classified as linear or branched on the basis of their chain architecture. The polymer chains in linear polymers have a long chain-like structure with minimal to no branching at all. Even if a polymer features large substituent groups on the monomer, which appear as branches to the skeleton, it is not considered a branched polymer. A branched polymer contains secondary polymer chains that arise from the main polymer chain. The branching occurs when the polymer growth shifts from...

An experiment is a planned activity carried out under controlled conditions. The purpose of an experiment is to investigate the relationship between two variables. When one variable causes change in another, we call the first variable the explanatory or independent variable. The affected variable is called the response or dependent variable. In a randomized experiment, the researcher manipulates values of the explanatory variable and measures the resulting changes in the response variable. The...

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...

Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...

In a beam of charged particles created by a heated cathode, the particles move at different speeds. However, many applications need a beam with uniform particle speeds. An arrangement known as a velocity selector uses electric and magnetic fields to pick particles with a particular speed from the beam.
A particle with charge q, speed v, and mass m enters an area from the top, where the magnetic and electric fields are perpendicular both to the particle's motion and to one another. The magnetic...