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Ch 22: Electric Charges and Forces
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 22: Electric Charges and ForcesProblema 68
Capitolo 22, Problema 68

An electric field E→=200,000i^\(\overrightarrow{E}\)=200,000\(\hat{i}\) N/C causes the point charge in FIGURE P22.68 to hang at an angle. What is θ?
Diagram showing a point charge of 25 nC and 2.0 g hanging at angle θ in an electric field of 200,000 N/C.

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Identify the forces acting on the point charge: The forces include the gravitational force \( F_g = mg \), the electric force \( F_e = qE \), and the tension \( T \) in the string. The tension has components in both the horizontal and vertical directions.
Write the force balance equations: In the vertical direction, the tension's vertical component balances the gravitational force, \( T \sin(\theta) = mg \). In the horizontal direction, the tension's horizontal component balances the electric force, \( T \cos(\theta) = qE \).
Divide the horizontal force equation by the vertical force equation to eliminate \( T \): \( \frac{T \cos(\theta)}{T \sin(\theta)} = \frac{qE}{mg} \). Simplify this to \( \tan(\theta) = \frac{qE}{mg} \).
Solve for \( \theta \): Use the inverse tangent function, \( \theta = \arctan\left(\frac{qE}{mg}\right) \).
Substitute the known values into the equation: Use the given electric field \( E = 200,000 \ \text{N/C} \), the charge \( q \), the mass \( m \), and the acceleration due to gravity \( g = 9.8 \ \text{m/s}^2 \) to calculate \( \theta \).

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Electric Field

An electric field is a region around a charged particle where other charged particles experience a force. It is represented by the symbol E and is measured in newtons per coulomb (N/C). The strength and direction of the electric field depend on the charge creating it and the distance from that charge.
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Intro to Electric Fields

Point Charge

A point charge is an idealized model of a charged object that has negligible size compared to the distances involved in the problem. It is characterized by its charge (positive or negative) and creates an electric field around it. The behavior of point charges in an electric field can be analyzed using Coulomb's law and the principles of electrostatics.
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Potential Due To Point Charges

Equilibrium of Forces

In the context of the problem, equilibrium of forces refers to the condition where the net force acting on the point charge is zero. This occurs when the gravitational force acting downward is balanced by the electric force acting upward, allowing the charge to hang at an angle θ. Analyzing these forces helps determine the angle at which the charge remains in equilibrium.
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Equilibrium
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