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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 37
Capitolo 22, Problema 37

Two 1.0 g spheres are charged equally and placed 2.0 cm apart. When released, they begin to accelerate at 150 m/s2. What is the magnitude of the charge on each sphere?

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Convert the given masses and distance into SI units. The mass of each sphere is 1.0 g, which is equivalent to 0.001 kg. The distance between the spheres is 2.0 cm, which is equivalent to 0.02 m.
Use Newton's second law of motion, \( F = ma \), to calculate the force acting on each sphere. Here, \( m = 0.001 \; \text{kg} \) and \( a = 150 \; \text{m/s}^2 \). Substitute these values into the equation to find the force \( F \).
Recognize that the force between the two charged spheres is due to Coulomb's law, which is given by \( F = \frac{k q^2}{r^2} \), where \( k = 8.99 \times 10^9 \; \text{N·m}^2/\text{C}^2 \) is Coulomb's constant, \( q \) is the charge on each sphere, and \( r = 0.02 \; \text{m} \) is the distance between the spheres.
Rearrange Coulomb's law to solve for \( q \): \( q = \sqrt{\frac{F r^2}{k}} \). Substitute the values of \( F \), \( r \), and \( k \) into this equation.
Simplify the expression to calculate the magnitude of the charge \( q \) on each sphere. Ensure that the units are consistent throughout the calculation.

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Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged objects. It 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 between them. This relationship is crucial for calculating the force acting on the spheres due to their charges.
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Percorso guidato
09:52
Coulomb's Law

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This principle allows us to relate the force experienced by the charged spheres to their acceleration, enabling the calculation of the force due to the electrostatic interaction.
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Percorso guidato
06:54
Intro to Forces & Newton's Second Law

Acceleration

Acceleration is the rate of change of velocity of an object. In this context, it indicates how quickly the spheres are speeding up due to the electrostatic force. Understanding acceleration is essential for applying Newton's Second Law to find the net force acting on the spheres, which can then be used to determine the charge on each sphere.
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Percorso guidato
05:47
Intro to Acceleration
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