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Una carga de \( 8 \times 10^{-8} \mathrm{C} \) ejerce una fuerza a otra carga de 0.1 N a una distancia de 7.5 m . ¿Cuál es el valor de la segunda carga? Nota: escriba su resultado con 4 decimales sin usar notación científica.

Ask by Cummings Young. in Colombia
Mar 15,2025

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La segunda carga es de \( 0.0078 \) C.

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The Deep Dive

Para resolver este problema, se puede utilizar la ley de Coulomb, que describe la fuerza entre dos cargas eléctricas. La fórmula es: \[ F = k \frac{|q_1 q_2|}{r^2} \] donde: - \( F \) es la fuerza entre las cargas (0.1 N), - \( k \) es la constante de Coulomb (\( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)), - \( q_1 \) es la primera carga (\( 8 \times 10^{-8} \, \text{C} \)), - \( q_2 \) es la segunda carga que queremos encontrar, - \( r \) es la distancia entre las cargas (7.5 m). Reorganizando la ecuación para despejar \( q_2 \): \[ q_2 = \frac{F r^2}{k |q_1|} \] Sustituyendo los valores conocidos: \[ q_2 = \frac{0.1 \, \text{N} \times (7.5 \, \text{m})^2}{8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \times 8 \times 10^{-8} \, \text{C}} \] Calculamos: \[ q_2 = \frac{0.1 \times 56.25}{8.99 \times 10^9 \times 8 \times 10^{-8}} \] \[ q_2 = \frac{5.625}{7.192 \times 10^2} \approx 0.007819 \] Por lo tanto, el valor de la segunda carga es aproximadamente: \[ \boxed{0.0078} \]

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