The figure shows four identical conducting spheres arranged in a square configuration. The spheres are equally spaced and have the same radius. The spheres are connected by conducting wires.
This arrangement of spheres is often used in electrical engineering to study the behavior of electric fields and charges. The spheres can be charged to different potentials, and the electric field between the spheres can be measured. This information can be used to calculate the capacitance of the system and the potential energy stored in the system.
Sphere Configuration
The four identical conducting spheres are arranged in a square configuration, with each sphere placed at one corner of the square. The spheres are suspended by insulating strings and are free to move.
Electrical Properties
The spheres are made of a conducting material, which means that they allow electric charges to flow freely across their surfaces. The spheres are initially uncharged, so they have the same electrical potential.
Charge Distribution
When the spheres are connected by a conducting wire, the charges on the spheres will redistribute themselves until they reach equilibrium. At equilibrium, the charges on the spheres will be distributed evenly, with each sphere having the same amount of charge.
Field Interactions
The charges on the spheres create an electric field around each sphere. The direction of the electric field is radially outward from each sphere. The strength of the electric field is proportional to the amount of charge on the sphere.
Capacitance
The capacitance of the system of four spheres is given by:
$$C = \frac4\pi\epsilon_0 ad$$
where:
- $$C$$ is the capacitance in farads
- $$a$$ is the radius of each sphere in meters
- $$d$$ is the distance between the centers of two adjacent spheres in meters
Potential Energy, The figure shows four identical conducting spheres
The potential energy of the system of four spheres is given by:
$$U = \frac12CV^2$$
where:
- $$U$$ is the potential energy in joules
- $$C$$ is the capacitance in farads
- $$V$$ is the potential difference between the spheres in volts
Applications
The system of four conducting spheres has a number of potential applications, including:
- Capacitors
- Electrostatic precipitators
- Lightning rods
Key Questions Answered: The Figure Shows Four Identical Conducting Spheres
What is the capacitance of the system of four conducting spheres?
The capacitance of the system of four conducting spheres is given by the following equation:
C = 4πε₀a/d
where:
- C is the capacitance in farads
- ε₀ is the permittivity of free space
- a is the radius of the spheres in meters
- d is the distance between the centers of the spheres in meters
What is the potential energy stored in the system of four conducting spheres?
The potential energy stored in the system of four conducting spheres is given by the following equation:
U = 1/2CV²
where:
- U is the potential energy in joules
- C is the capacitance in farads
- V is the potential difference between the spheres in volts
