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What is the electric potential inside a conducting spherical shell?
The electric potential inside a conducting spherical shell is zero.
What is the relationship between the electric force and potential in a system with spherical symmetry?
In a system with spherical symmetry, the electric force is directly related to the potential. The electric force is the gradient of the electric potential, meaning that the force is stronger where the potential changes more rapidly. This relationship helps to describe how charges interact in a spherical system.
What is the relationship between the electric potential and electric field according to the equations V kq/r and E kq/r2?
The relationship between electric potential (V) and electric field (E) is that the electric field is the negative gradient of the electric potential. This means that the electric field is the rate of change of the electric potential with respect to distance. The equations V kq/r and E kq/r2 show that the electric field is inversely proportional to the square of the distance from the charge, while the electric potential is inversely proportional to the distance from the charge.
Electric charge is uniformly distributed on the surface of a spherical balloon. Show how electric intensity and electric potential vary (a) on the surface (b) inside and (c) outside?
(a) On the surface of the balloon, the electric intensity is perpendicular to the surface and is constant. The electric potential varies across the surface with the highest value at the region of highest charge density. (b) Inside the balloon, the electric intensity and potential will be zero since the Gaussian surface does not enclose any charge. (c) Outside the balloon, the electric intensity decreases inversely with the square of the distance from the center of the balloon, while the electric potential also decreases with distance, following a similar inverse square law.
What is the relationship between the electric potential of a charged rod and its distance from a point in space?
The electric potential of a charged rod decreases as the distance from a point in space increases. This relationship is described by the inverse square law, where the electric potential is inversely proportional to the square of the distance from the charged rod.
What is the electric potential inside a conducting spherical shell?
The electric potential inside a conducting spherical shell is zero.
What is the relationship between the electric force and potential in a system with spherical symmetry?
In a system with spherical symmetry, the electric force is directly related to the potential. The electric force is the gradient of the electric potential, meaning that the force is stronger where the potential changes more rapidly. This relationship helps to describe how charges interact in a spherical system.
What is the relationship between the electric potential and electric field according to the equations V kq/r and E kq/r2?
The relationship between electric potential (V) and electric field (E) is that the electric field is the negative gradient of the electric potential. This means that the electric field is the rate of change of the electric potential with respect to distance. The equations V kq/r and E kq/r2 show that the electric field is inversely proportional to the square of the distance from the charge, while the electric potential is inversely proportional to the distance from the charge.
Electric charge is uniformly distributed on the surface of a spherical balloon. Show how electric intensity and electric potential vary (a) on the surface (b) inside and (c) outside?
(a) On the surface of the balloon, the electric intensity is perpendicular to the surface and is constant. The electric potential varies across the surface with the highest value at the region of highest charge density. (b) Inside the balloon, the electric intensity and potential will be zero since the Gaussian surface does not enclose any charge. (c) Outside the balloon, the electric intensity decreases inversely with the square of the distance from the center of the balloon, while the electric potential also decreases with distance, following a similar inverse square law.
What is the relationship between the electric potential of a charged rod and its distance from a point in space?
The electric potential of a charged rod decreases as the distance from a point in space increases. This relationship is described by the inverse square law, where the electric potential is inversely proportional to the square of the distance from the charged rod.
What are factors that determine the size of the electric potential and electric potential energy?
The size of the electric potential is determined by the amount of charge creating the electric field and the distance from the charge. The electric potential energy depends on the charge of the object and its position in the electric field, as well as the electric potential at that point.
What is the electric field outside a charged spherical shell?
Outside a charged spherical shell, the electric field behaves as if all the charge is concentrated at the center of the shell. This is known as Gauss's Law for a spherical surface, which states that the electric field at a distance r from the center of a charged spherical shell is equivalent to that of a point charge with the same total charge as the shell at the center. Therefore, the electric field outside a charged spherical shell decreases with the square of the distance from the center of the shell.
What is the relationship between electric potential and electric field in a given system?
In a given system, the electric potential is directly related to the electric field. The electric field is the rate of change of electric potential with respect to distance. In other words, the electric field points in the direction of decreasing potential.
What are the properties of electric fields within a spherical volume of space?
The properties of electric fields within a spherical volume of space include the field being radially outward from the center of the sphere, decreasing in strength as the distance from the center increases, and being uniform at any given distance from the center.
What is the electric potential inside a parallel-plate capacitor and how does it relate to the charge and separation distance of the plates?
The electric potential inside a parallel-plate capacitor is directly proportional to the charge on the plates and inversely proportional to the separation distance between the plates. This means that as the charge on the plates increases, the electric potential also increases, and as the separation distance between the plates decreases, the electric potential increases.
How to find electric potential in a given system?
To find the electric potential in a given system, you can use the formula V kQ/r, where V is the electric potential, k is the Coulomb's constant, Q is the charge, and r is the distance from the charge. Calculate the electric potential at different points in the system by plugging in the values for charge and distance.
How is electric potential energy similar to gravitational potential energy?
Electric potential energy, like gravitational potential energy, represents the stored energy an object has due to its position or configuration in a field. Both types of potential energy depend on the object's distance or position relative to a source (electric charge for electric potential energy and mass for gravitational potential energy). The formulas for calculating electric and gravitational potential energy have similar mathematical forms involving distance and a constant.
