A charged isolated metal sphere of diameter is an intriguing concept in electromagnetism that reveals the intricate interplay between electric field, potential, and energy. This sphere holds significant importance in understanding the behavior of electric charges and their practical applications.
Delving into the characteristics of a charged isolated metal sphere, we explore the concept of electric field and its direction around the sphere. Formulas are provided to calculate electric field strength, elucidating the relationship between charge and field strength.
Charged Isolated Metal Sphere
A charged isolated metal sphere is a spherical conductor with a net electric charge. It has several important characteristics:
- The charge is distributed uniformly over the surface of the sphere.
- The electric field inside the sphere is zero.
- The electric field outside the sphere is radial and points away from the sphere if the charge is positive, and towards the sphere if the charge is negative.
The analysis of charged isolated metal spheres is important in various fields of physics, including electrostatics, electronics, and medical imaging.
Electric Field
The electric field around a charged isolated metal sphere is given by:
$$E = k\fracqr^2$$
where:
- $E$ is the electric field strength
- $k$ is Coulomb’s constant ($8.98755 \times 10^9 \text N\cdot\textm^2/\textC^2$)
- $q$ is the charge on the sphere
- $r$ is the distance from the center of the sphere
The electric field strength is inversely proportional to the square of the distance from the center of the sphere. This means that the electric field is strongest near the sphere and becomes weaker as the distance increases.
Electric Potential, A charged isolated metal sphere of diameter
The electric potential at a point outside a charged isolated metal sphere is given by:
$$V = k\fracqr$$
where:
- $V$ is the electric potential
- $k$ is Coulomb’s constant
- $q$ is the charge on the sphere
- $r$ is the distance from the center of the sphere
The electric potential is directly proportional to the charge on the sphere and inversely proportional to the distance from the center of the sphere.
Equipotential surfaces are surfaces where the electric potential is constant. For a charged isolated metal sphere, the equipotential surfaces are concentric spheres centered on the sphere.
Capacitance
The capacitance of a charged isolated metal sphere is given by:
$$C = 4\pi\varepsilon_0r$$
where:
- $C$ is the capacitance
- $\varepsilon_0$ is the permittivity of free space ($8.85 \times 10^-12 \text F/m$)
- $r$ is the radius of the sphere
The capacitance of a sphere is directly proportional to its radius. This means that larger spheres have greater capacitance than smaller spheres.
Energy Stored
The energy stored in a charged isolated metal sphere is given by:
$$U = \frac12CV^2$$
where:
- $U$ is the energy stored
- $C$ is the capacitance
- $V$ is the electric potential
The energy stored in a sphere is directly proportional to the square of the charge on the sphere. This means that the more charge stored on a sphere, the greater the energy stored.
Applications
Charged isolated metal spheres have a wide range of applications, including:
- Capacitors
- Lightning rods
- Medical imaging
- Particle accelerators
FAQ Overview: A Charged Isolated Metal Sphere Of Diameter
What is the significance of a charged isolated metal sphere?
A charged isolated metal sphere is significant because it allows us to study the behavior of electric charges in a controlled environment, free from external influences.
How does the charge on the sphere affect the electric field?
The charge on the sphere is directly proportional to the electric field strength. As the charge increases, the electric field strength also increases.
What is the relationship between electric potential and electric field?
Electric potential is the amount of electrical potential energy per unit charge. It is related to the electric field by the equation V = Ed, where V is the electric potential, E is the electric field strength, and d is the distance from the sphere.
