A charged cork ball of mass 1.00 g is suspended on a light string in the presence of a uniform e

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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 $\mathrm{P} 23.55$ . When $\mathbf{E}=(3.00 \hat{\mathbf{i}}+5.00 \hat{\mathbf{j}}) \times$ $10^{5} \mathrm{N} / \mathrm{C},$ 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

Electrostatic Force

An object with electric charge experiences a force when placed in an electric field. The magnitude and direction of this force are determined by the product of the charge and the electric field vector, expressed as F = qE. This concept is crucial when analyzing the effects an external electric field has on charged objects, especially in equilibrium scenarios.

Gravitational Force

All objects with mass experience gravitational force, which acts downward toward the center of the Earth. This force is quantified as mg, where m is the mass and g is the acceleration due to gravity. In problems involving suspended objects, gravitational force must be balanced by other forces for the object to remain in equilibrium.

Equilibrium of Forces

For an object to be in static equilibrium, the vector sum of all forces acting on it must be zero. This principle applies in both horizontal and vertical directions. In scenarios where additional forces are present, like an electric force, the conditions of equilibrium are used to set up equations that can solve for unknown quantities such as charge or tension.

Vector Decomposition and Trigonometry

When forces are applied at angles, breaking them down into orthogonal components (typically horizontal and vertical) is essential for analyzing the equilibrium conditions. Trigonometric functions (sine and cosine) are used to relate the magnitude of a force to its components along these directions. This method simplifies the analysis of forces in systems where multiple directional influences are present, such as in a suspended charged object influenced by gravity and an electric field.

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