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