Pregunta
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wo spheres of radii 3 cm and 8 cm are charged
ith and of electricity
spectively. If they are joined by a wire, how
uch charge will flow from one to the othet

Ask by Chen Tran. in India
Jan 26,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

Approximately 1.45 × 10⁻⁹ C of charge flows from the 8 cm sphere to the 3 cm sphere.

Solución

When two conducting spheres are connected by a wire, charge flows between them until their electric potentials are equal. Here’s how to determine the amount of charge that flows:

Given:

  • Sphere 1: Radius cm, Charge C
  • Sphere 2: Radius cm, Charge C

Step-by-Step Solution:

  1. Electric Potential of a Sphere:
    The electric potential of a charged sphere is given by:
    where:
    • is Coulomb’s constant.
    • is the charge.
    • is the radius of the sphere.
  2. Equalizing Potentials:
    When the spheres are connected, their potentials become equal:
    Simplifying:
  3. Conservation of Charge:
    The total charge before and after connecting the spheres remains the same:
  4. Solving for :
    Substitute into the conservation equation:
  5. Determining Charge Flow:
    • Sphere 2 (initially 16 × 10⁻⁹ C) transfers charge to reach :
    • Sphere 1 (initially 4 × 10⁻⁹ C) gains this charge:

Final Answer:

Approximately 1.45 × 10⁻⁹ C of charge flows from the 8 cm sphere to the 3 cm sphere.

Respondido por UpStudy AI y revisado por un tutor profesional

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The Deep Dive

When you connect two charged spheres with a wire, charge will flow from one sphere to the other until they reach the same electric potential. The potential of each charged sphere can be calculated using the formula , where is Coulomb’s constant, is the charge, and is the radius of the sphere.
For the first sphere, and for the second sphere, . After simplifying, you will find that both spheres will ultimately stabilize at the same potential, leading to a transfer of charge until equilibrium is reached.
Upon performing the specific calculations, you’ll find that a net charge will flow from the sphere with the higher charge density (smaller radius) to the larger radius sphere until their potentials equalize, setting the stage for fun electrostatics!
Remembering to double-check calculations for errors can save you from common mistakes in understanding potential differences and charge distribution!

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