# Scalar vs. Vector

Created: 5/16/2020

Last Updated: 07/06/2023

Definition

In physics, scalar quantities represent physical quantities that have magnitude only, whereas vector quantities have both magnitude and direction.

Key Difference: The key trait of a vector quantity is its directionality, which plays a crucial role in many real-world phenomena.

Examples:

Power in Electrical Circuits (Scalar): Power is a scalar quantity as it only possesses magnitude information. When calculating the total power loss in a circuit, we can simply sum the individual power losses since they are scalars. For instance, if we have resistors connected in series, we can add up their individual power dissipations to determine the total power loss in the circuit.

Electromagnetic (EM) Waves (Vector): Electromagnetic waves, such as light, are vector quantities. When combining two incident EM waves at a specific point, we need to consider both the amplitudes and relative phase information. The amplitude and phase of the combined wave depend on the direction and path differences of the individual waves. For example, when two light waves with different phases and amplitudes meet at a point, the resulting amplitude is determined by the phase difference between them. This phenomenon is observed in interference patterns, where constructive interference occurs when the waves are in phase and destructive interference occurs when they are out of phase.

Understanding the distinction between scalar and vector quantities is essential in various fields of science and engineering, including physics, electrical engineering, and signal processing. It allows us to accurately describe and analyze physical phenomena based on their magnitude and direction components.