Two positive charges with magnitude q and 2 q sit at points...

Two positive charges with magnitude $q$ and $2 q$ sit at points $(1,0)$ and $(0,1)$ on the $x$ - and $y$-axis, respectively. Which figure best represents the total electric field at the origin?
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) $\mathrm{D}$
(E) $\mathrm{E}$

Key Concepts

Electric Field

The electric field is a vector field that represents the force per unit charge exerted on a test charge at any point in space. It is a fundamental concept in electromagnetism, and its magnitude and direction can be calculated based on the source charges using Coulomb's law.

Point Charge

A point charge is an idealization where the entirety of a charge is concentrated at a single point in space. The electric field created by a point charge is radial and its magnitude decreases with the square of the distance from the charge, as described by Coulomb's law.

Superposition Principle

The superposition principle states that when multiple charges create electric fields, the total field at any point is the vector sum of the fields produced by each individual charge. This principle allows for the analysis of complex charge configurations by considering the contribution of each charge separately.

Vector Addition

Vector addition is a mathematical method used to combine multiple vectors, taking into account both their magnitudes and directions. In the context of electric fields, it is essential because the field from each charge must be resolved into its components before being summed to yield the total electric field.

Coordinate System and Field Representation

A coordinate system is used to define positions in space and to resolve vector quantities into their components. Graphical representations of electric fields, such as field diagrams, help visualize the direction and relative strength of the field, making it easier to understand how different charges influence the total electric field at a point.

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