A small sphere of charge q=+68 μC and mass m=5.8 g is attached to a light string and placed in a

step 1 Harris to Grange, let's start our discussion electric field. Now suppose you have a sphere of ch

A small sphere of charge q=+68 μC and mass m=5.8 g is...

A small sphere of charge $q=+68 \mu \mathrm{C}$ and mass $m=5.8 \mathrm{g}$ is attached to a light string and placed in a uniform electric field $\overrightarrow{\mathrm{E}}$ that makes an angle $\theta=37^{\circ}$ with the horizontal. The opposite end of the string is attached to a wall and the sphere is in static equilibrium when the string is horizontal as in Figure $\mathrm{P} 15.22$ . (a) Construct a free body diagram for the sphere. Find (b) the magnitucle of the electric field and (c) the ten- sion in the string.

Key Concepts

Tension Force

The tension force is the force transmitted through a string, rope, or similar object when it is pulled tight by forces acting at each end. In problems involving charges suspended by a string, understanding the tension force is important because it balances the other forces (like gravitational force and electric force) acting on the object, keeping it in static equilibrium.

Uniform Electric Field

A uniform electric field is one in which the magnitude and direction of the electric field are constant at every point in space. This simplifies calculations because the force acting on a charged particle within the field remains constant, allowing straightforward application of equilibrium conditions and force analysis.

Electric Force

The electric force is the force exerted on a charged object when it is placed in an electric field. It is calculated by multiplying the magnitude of the charge by the magnitude of the electric field. This concept is essential when analyzing the behavior of charged particles in external fields, as it directly influences the net force acting on the particle.

Static Equilibrium

Static equilibrium refers to the state of an object when it is at rest and the net forces and net moments acting on it are zero. This means that the sum of all horizontal forces and vertical forces must independently equal zero. Understanding static equilibrium is crucial for analyzing systems where objects are suspended or supported, allowing the determination of unknown forces such as tensions or applied fields.

Free Body Diagram

A free body diagram is a schematic representation used to visualize the forces acting on an object. It involves drawing the object as a point or simple shape and representing all forces—such as gravitational force, tension, and any applied forces—with vector arrows. The diagram helps in setting up equations based on the balance of forces in various directions, which is essential for solving problems involving equilibrium.

Force Decomposition

Force decomposition is the process of breaking a force vector into its components along perpendicular directions, commonly horizontal and vertical. This is typically done using trigonometric functions like sine and cosine. It simplifies the application of equilibrium conditions because forces along orthogonal directions can be analyzed separately, making it easier to solve for unknown quantities in the problem.

Transcript

Please give Ace some feedback