How to Find the Direction of an Electric Field Using the Right Hand Rule | Physics | Study.com

Steps to Find the Direction of an Electric Field Using the Right Hand Rule

Step 1: Identify the direction of the magnetic field, {eq}\vec{B} {/eq}, and of propagation, {eq}\vec{v} {/eq}

Step 2: Using your right hand, extend your thumb and pointer finger in an “L”-shape, and then extend your middle finger to point outward from the base of the “L”

Step 3: Align your pointer finger along {eq}\vec{B} {/eq} and your middle finger along {eq}\vec{v} {/eq}.

Step 4: Observe the direction these previous steps have left your thumb pointing in as the direction of {eq}\vec{E} {/eq}

Equations & Definitions for Finding the Direction of an Electric Field Using the Right Hand Rule

Waves: A wave is a transfer of energy involving an oscillation of a medium or field. Waves are classified as either

• Transverse: where the oscillations occur in a perpendicular direction to the propagation, or
• Longitudinal: where oscillations occur parallel to the direction of propagation.

For example, a wave of water in the ocean is transverse since the peaks and troughs occur in the vertical direction while the wave propagates horizontally toward the shore. In contrast, a sound wave is longitudinal since the air is being compressed and expanded in the direction in which the sound is traveling.

Visual representation of the difference between a longitudinal wave and transverse wave

Light Wave: A light wave, often called an electromagnetic wave in reference to its constituent fields, is a transverse wave made up of an oscillating electric field perpendicular to an oscillating magnetic field. The wave propagates in a direction perpendicular to both the electric field and the magnetic field. Based only on this criterion, there would be two possible directions for the light to propagate. However, light waves must satisfy a set of physics equations called Maxwell’s equations.

Maxwell’s Equations: This dictates how electric and magnetic fields interact. When these equations are solved in free space only one of these directions is a possible direction of propagation, and to find it we can use a trick called the right-hand rule (RHR).

Light is a transverse wave of electric and magnetic fields

The Right-Hand Rule: Using your right hand, extend your thumb and pointer finger to form an “L”-shape, then extend your middle finger outward from the base of this “L” (see figure 2). These 3 fingers should now form a set of 3-dimensional axes, that is, you should now be able to put your hand on the corner of a box and have each of these 3 fingers lie on a different side of the box. Once you have your RHR axes rotate your hand until your thumb is aligned with the direction of the electric field and your pointer finger is aligned with the direction of the magnetic field. Then the resulting direction of your middle finger is the direction of propagation that satisfies Maxwell’s equations.

Diagram of using your right hand to find relative directions of the electric and magnetic fields, and propagation of a light wave