A charged cork ball of mass 1.00 g is suspended on a light...

A charged cork ball of mass $1.00 \mathrm{~g}$ is suspended on a light string in the presence of a uniform electric field, as shown in Figure $\mathrm{P} 23.53$. When $\mathbf{E}=(3.00 \mathbf{i}+$ $5.00 \mathbf{j}) \times 10^{5} \mathrm{~N} / \mathrm{C}$, the ball is in equilibrium at $\theta=37.0^{\circ} .$ Find (a) the charge on the ball and (b) the tension in the string.

Key Concepts

Equilibrium Analysis

Equilibrium analysis involves setting the sum of all forces acting on an object to zero so that the object remains at rest or in uniform motion. In problems involving suspended objects in an electric field, this analysis helps to determine unknown quantities such as tension or charge by balancing the forces in each coordinate direction.

Gravitational Force

Gravitational force is the force exerted by the Earth on any mass, acting downwards. It is calculated as the product of mass and the acceleration due to gravity, and it plays a crucial role in balancing other forces in systems involving suspended objects.

Vector Decomposition

Vector decomposition is the process of breaking a vector into its component parts along chosen axes (typically horizontal and vertical). This technique is essential in physics as it allows for the separate analysis of forces acting in different directions, facilitating the application of equilibrium conditions.

Electric Force

The electric force is the force exerted on a charged object when placed in an electric field. It is given by the product of the charge and the electric field strength, and its direction is determined by the sign of the charge and the orientation of the field.

Uniform Electric Field

A uniform electric field is one where the magnitude and direction of the electric field are constant in space. This simplifies analysis because the force experienced by a charge is the same regardless of its position within the field.

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