A small, plastic sphere of mass m=100 g is attached to a...

A small, plastic sphere of mass $m=100 \mathrm{g}$ is attached to a string as shown in Figure $\mathrm{P} 17.45$ There is an electric field of $100 \mathrm{N} / \mathrm{C}$ directed along the $+x$ direction. If the string makes an angle $\theta=30^{\circ}$ with the $y$ axis, what is the charge on the sphere?

Key Concepts

Force Decomposition

Force decomposition involves breaking down a force vector into its perpendicular components, typically along coordinate axes like the x and y directions. This process simplifies the analysis of forces acting at angles, allowing for independent resolution of forces and easier application of equilibrium equations.

Static Equilibrium

Static equilibrium refers to the condition where the sum of all forces acting on an object is zero, meaning the object is at rest or moves with constant velocity. This principle is essential in solving problems involving balance of forces, such as determining the necessary charge on an object so that electrical and gravitational forces are counteracted.

Free-Body Diagram

A free-body diagram is a schematic illustration that depicts all external forces acting on an object. By clearly showing forces such as gravitational force, tension, and any applied electric force, this tool helps in setting up the correct equilibrium equations needed to analyze the situation, ensuring that all relevant forces are accounted for in problem-solving.

Electric Field

An electric field is a region in space where a charge experiences an electric force. It is defined as the force per unit charge, and its direction is the same as the direction that a positive test charge would be pushed. This concept is crucial for understanding how charges interact with their surroundings and how they are influenced by external electric fields.

Electric Force

Electric force is the force exerted on a charged particle placed in an electric field, calculated by multiplying the charge by the electric field strength. This force dictates the motion or equilibrium condition of the object when subjected to the field, and is one of the core forces considered in electromagnetism.

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