A charge of 63.0 nC is located at a distance of 3.40 cm from...

A charge of $63.0 \mathrm{nC}$ is located at a distance of $3.40 \mathrm{cm}$ from a charge of $-47.0 \mathrm{nC}$. What are the $x$ - and y-components of the electric field at a point $P$ that is directly above the $63.0 \mathrm{nC}$ charge at a distance of $1.40 \mathrm{cm} ?$ Point $P$ and the two charges are on the vertices of a right triangle.

Key Concepts

Coulomb’s Law

Coulomb’s Law quantifies the force between two point charges by stating that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This fundamental principle allows us to determine how charges interact and is the foundation for calculating the electric field produced by a point charge.

Electric Field of a Point Charge

The electric field produced by a point charge is defined as the force per unit positive test charge that would be exerted on it, and is given by the relation E = k|q|/r², where k is Coulomb's constant, q is the charge, and r is the distance from the charge. The direction of the field depends on the sign of the charge, pointing radially outward for positive charges and inward for negative charges.

Superposition Principle

The superposition principle states that when multiple charges are present, the total electric field at any point is the vector sum of the electric fields produced by each individual charge independently. This principle makes it possible to analyze complex arrangements of charges by calculating the separate contributions and then summing their vector components.

Vector Decomposition

Vector decomposition is the process of breaking a vector into its components along predefined axes, typically using sine and cosine functions when dealing with angles. This technique is crucial in physics for analyzing quantities like electric fields or forces that have both magnitude and direction, allowing calculations to be performed along the x- and y-axes separately.

Right Triangle Geometry

Right triangle geometry involves using the relationships between the sides and angles of a right triangle, often employing trigonometric ratios such as sine, cosine, and tangent. This approach is essential in physics problems to relate spatial distances and to resolve vectors into their horizontal and vertical components based on the geometry of the situation.

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