Pregunta
upstudy study bank question image url

20.2 Calculate the net electrostatio force that and exert on .

Ask by Page Cummings. in South Africa
Mar 14,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

The net electrostatic force on is downward.

Solución

We will illustrate a complete solution by assuming the following configuration. (In your particular textbook the numbers and positions may differ. In our example the values below are assumed.)
Assume that three point charges are located at the vertices of an isosceles “horizontal‐base” triangle as follows:
• Charge is at point .
• Charge is at point .
• Charge is at point .
When a negative charge is attracted toward a positive charge the force on the negative charge points toward the positive charge. Thus the force on due to (denoted ) points from toward , and the force on due to (denoted ) points from toward .
Below are the step‐by‐step calculations.

1. Determine the Distances

The distance from to either or is given by the distance formula. For example, for to :
Similarly,

2. Compute the Magnitudes of the Forces

Coulomb’s law gives the magnitude of the force between two point charges:
where . First, express all charges in Coulombs:
Since the distance squared is
the magnitude of the force exerted by on is
Calculate the product in the numerator:
Thus,
Multiply the numbers:
so
Because of symmetry, the force from on has the same magnitude:

3. Determine the Directions and Components of the Forces

Force :
The force on due to points from at toward at . The vector from to is
Its magnitude is
Thus the unit vector in the direction from to is
So, the vector force is
Force :
The force on due to points from at toward at . The vector from to is
Its magnitude is also
Thus the unit vector is
Then,

4. Find the Net Force on

The net force on is the vector sum
Adding the components:
  • -component:
  • -component:
Thus,
[
\vec{F}_{net} = \left(0

Respondido por UpStudy AI y revisado por un tutor profesional

error msg
Explicar
Simplifique esta solución

Extra Insights

To calculate the net electrostatic force that charges and exert on charge , you first need to determine the individual forces using Coulomb’s Law, which states that the force between two point charges is given by:
where is Coulomb’s constant ( ), and are the magnitudes of the charges, and is the distance between them. Once you find (the force exerted by on ) and (the force exerted by on ), you can determine the direction of these forces based on the signs of the charges. The net force is found by vectorially adding and .
From here, remember that forces acting in the same direction will add together, while forces acting in opposite directions will subtract.
Lastly, make sure to double-check your distances and charge values, as miscalculations can significantly alter your results. Keeping track of the signs for attraction and repulsion based on charge polarity is essential for accurate computations!

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad