A small, 2.00 g plastic ball is suspended by a 20.0 -m-long...

A small, 2.00 g plastic ball is suspended by a 20.0 -m-long string in a uniform electric field as shown in Figure $\mathrm{P} 23.54$ . If the ball is in equilibrium when the string makes a $15.0^{\circ}$ angle with the vertical, what is the net charge on the ball?

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Key Concepts

Static Equilibrium

Static equilibrium is the condition in which an object remains at rest because the net force acting on it is zero. In such problems, the sum of all forces in every direction must cancel, which allows analysts to set up balance equations that equate opposing forces.

Decomposition of Forces

Decomposition of forces involves breaking a force into its perpendicular components, typically along horizontal and vertical axes. This technique simplifies the analysis of forces acting at angles by letting one treat each directional component independently to set up equations for force balance.

Uniform Electric Field and Electric Force

In a uniform electric field, a charged object experiences an electric force defined by the product of its net charge and the field strength. This concept is crucial for understanding how electric fields influence charged bodies, similar to how gravitational fields act on masses.

Gravitational Force

Gravitational force is the attractive force exerted by the Earth on an object, calculated as the product of the object's mass and the acceleration due to gravity. This force is a fundamental element in mechanical equilibrium problems, providing the vertical component that must be balanced by other forces.

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