Two tiny spheres of mass 6.80 mg carry charges of equal...

Two tiny spheres of mass 6.80 mg carry charges of equal magnitude, 72.0 nC, but opposite sign. They are tied to the same ceiling hook by light strings of length 0.530 m. When a horizontal uniform electric field $E$ that is directed to the left is turned on, the spheres hang at rest with the angle $\theta$ between the strings equal to 58.0$^\circ \space (\textbf{Fig.P21.74}$). (a) Which ball (the one on the right or the one on the left) has positive charge? (b) What is the magnitude $E$ of the field?

Key Concepts

Coulomb's Law

Coulomb's law describes the magnitude of the electrostatic force between two point charges. The law states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance separating them. This law is fundamental in determining the interactions between multiple charged bodies in a system.

Electric Field and Electric Force

An electric field is a region surrounding a charged object where other charged objects experience a force. The force experienced by a test charge in an electric field is proportional to the magnitude of the charge and the magnitude of the field, given by F = qE. This principle is crucial for understanding how charged particles respond to external electric fields in various configurations.

Vector Decomposition

Vector decomposition involves breaking forces into their perpendicular components, typically horizontal and vertical, so that the complex interaction of forces at an angle can be analyzed separately along each axis. This technique simplifies the solving of equilibrium conditions by enabling the separate analysis of the forces acting in each direction.

Static Equilibrium

Static equilibrium refers to the state in which an object remains at rest because the net force acting on it is zero. This concept is essential in mechanics as it allows us to set up equations by balancing forces in all directions, which can then be used to determine unknown forces or angles in a system where multiple forces like gravitational, tension, and electric forces are present.

Transcript

Please give Ace some feedback