Skip to main content
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 42a
Capitolo 22, Problema 42a

Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed 10 cm apart, B experiences an electric force of 0.45 N. What is the charge on A?

Guida verificata passo dopo passo
1
Step 1: Start by identifying the relevant formula for the electric force between two charges. The formula is Coulomb's Law: F = k * (q_1 * q_2) / r^2, where F is the electric force, k is Coulomb's constant (8.99 × 10^9 \, N \, m^2 / C^2), q_1 and q_2 are the charges, and r is the distance between the charges.
Step 2: Assign the given values to the variables. The force F is 0.45 N, the distance r is 10 cm (convert to meters: r = 0.1 \, m), and the relationship between the charges is q_A = 2q_B.
Step 3: Substitute q_A = 2q_B into Coulomb's Law. The equation becomes: F = k * (2q_B * q_B) / r^2, which simplifies to F = k * (2q_B^2) / r^2.
Step 4: Rearrange the equation to solve for q_B. The equation becomes: q_B^2 = (F * r^2) / (2k). Take the square root to find q_B: q_B = sqrt((F * r^2) / (2k)).
Step 5: Once q_B is calculated, use the relationship q_A = 2q_B to find the charge on A. This completes the solution.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
5m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

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 law is fundamental for calculating the electric force acting between charged objects, which is essential for solving the problem at hand.
Video consigliato:
Percorso guidato
09:52
Coulomb's Law

Electric Charge

Electric charge is a property of matter that causes it to experience a force when placed in an electromagnetic field. Charges can be positive or negative, and like charges repel while opposite charges attract. In this scenario, understanding the relationship between the charges of objects A and B is crucial for determining the charge on A based on the given force experienced by B.
Video consigliato:
Percorso guidato
05:37
Electric Charge

Force Calculation

The calculation of force in physics often involves using formulas that relate mass, acceleration, and in this case, electric force. For charged objects, the force can be calculated using Coulomb's Law. Knowing the force experienced by B allows us to backtrack and find the charge on A, given that A has twice the charge of B.
Video consigliato:
Percorso guidato
06:09
Work Done by a Constant Force
Pratica correlata
Domanda del libro di testo

A 0.10 g honeybee acquires a charge of +23 pC while flying. What electric field (strength and direction) would allow the bee to hang suspended in the air?

1671
views
Domanda del libro di testo

What is the force F on the 1.0 nC charge at the bottom in FIGURE P22.47? Give your answer in component form.

4732
views
5
rank
Domanda del libro di testo

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?

1525
views
Domanda del libro di testo

A +2.0 nC charge is at the origin and a −4.0 nC charge is at x = 1.0 cm. Would the net force be zero for an electron placed at the same position? Explain.

2288
views
Domanda del libro di testo

A 3.00-cm-long spring has a small plastic bead glued to each end. Charging each bead to −25 nC expands the spring by 0.50 cm. What is the value of the spring constant?

1496
views
Domanda del libro di testo

What is the force F on the 8.0 nC charge in FIGURE P22.44? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the +x-axis.

2719
views