A point charge of mass 0.081 kg and charge +6.77 μC is suspended by a thread between the vertica

step 1 Hi, here in this given problem, these are the two plates of a charged capacitor having a gap D.

A point charge of mass 0.081 kg and charge +6.77 μC is...

A point charge of mass 0.081 kg and charge $+6.77 \mu C$ is suspended by a thread between the vertical parallel plates of a parallel-plate capacitor, as shown in Figure $20-30$. (a) If the charge deflects to the right of vertical, as indicated in the figure, which of the two plates is at the higher electric potential? (b) If the angle of deflection is $22^{\circ}$, and the separation between the plates is $0.025 \mathrm{m},$ what is the potential difference between the plates?

Key Concepts

Force Equilibrium on a Charged Particle

This concept involves analyzing the balance of forces acting on a charged particle when it is suspended or in motion within an electric field. In equilibrium, the net force on the particle is zero, meaning that all forces such as the gravitational force and the electric force cancel each other out. Understanding this equilibrium is key to determining the behavior and position of the particle in the field.

Force Resolution Using Trigonometry

Force resolution involves breaking a force vector into its components along mutually perpendicular directions, typically using trigonometric functions. This allows for the examination of equilibrium conditions and the calculation of unknown quantities like the electric field magnitude or the potential difference, based on the observable deflection angle of a charged particle.

Electric Field in a Parallel-Plate Capacitor

This concept refers to the uniform electric field that exists between two parallel plates when a potential difference is applied. The electric field has a consistent magnitude and direction throughout the space between the plates, pointing from the positively charged plate to the negatively charged plate. It is fundamental for understanding how charged particles will experience a force when placed between the plates.

Electric Potential Difference

The electric potential difference is the work done per unit charge to move a charge between two points in an electric field. In the context of a parallel-plate capacitor, it relates directly to the electric field strength and the separation between the plates. This concept is critical for analyzing how the energy state of a charge changes as it moves within the field.

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