Three charges, q1=+q, q2=-q, and q3=+q, are at the vertices...

Three charges, $q_{1}=+q, q_{2}=-q,$ and $q_{3}=+q,$ are at the vertices of an equilateral triangle, as shown in Figure $19-31$. (a) Rank the three charges in order of increasing magnitude of the electric force they experience. Indicate ties where appropriate. (b) Give the direction angle, $\theta$, of the net electric force experienced by charge $1 .$ Note that $\theta$ is measured counterclockwise from the positive $x$ axis. (c) Repeat part (b) for charge 2 . (d) Repeat part (b) for charge 3 .

Three charges, $q_{1}=+q, q_{2}=-q,$ and $q_{3}=+q,$ are at the vertices of an equilateral triangle, as shown in Figure $19-31$. (a) Rank the three charges in order of increasing magnitude of the electric force they experience. Indicate ties where appropriate. (b) Give the direction angle, $\theta$, of the net electric force experienced by charge $1 .$ Note that $\theta$ is measured counterclockwise from the positive $x$ axis.
(c) Repeat part (b) for charge 2 . (d) Repeat part (b) for charge 3 .

Key Concepts

Rank Comparison of Electric Force Magnitudes

When comparing the forces experienced by different charges in a configuration, one must consider both magnitude and vector direction. The ranking process involves calculating or inferring the net force magnitude on each charge, often by analyzing the contributions from other charges and using principles such as cancellation due to symmetry, to establish a relative ordering in terms of force intensity.

Symmetry in Charge Configurations

Symmetry in the arrangement of charges, such as an equilateral triangle, plays a significant role in simplifying the problem. A symmetric configuration often leads to cancellations or amplifications of certain force components, making it easier to predict the direction of the net force and compare the magnitudes of forces on different charges.

Electric Force Direction and Components

Determining the direction of the net electric force involves calculating the angle that the resultant vector makes with a reference axis. This is typically done by using trigonometric functions, where the net force is resolved into x- and y-components, and the direction angle is then computed using inverse trigonometric relations.

Coulomb's Law

Coulomb's Law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. This fundamental law provides the basis for calculating the magnitude and direction of the electric force exerted by one charge on another and is central to understanding interactions in electrostatics.

Vector Addition of Forces

Since forces are vector quantities, when multiple charges exert forces on one another, the net force on a given charge is the vector sum of the individual forces. This requires decomposing the forces into their components along mutually perpendicular axes and then combining these components to determine both the overall magnitude and direction of the net force.

Please give Ace some feedback