For a charged spherical ball, electrostatic potential inside the ball varies with π as $V=2ππ^2+π$. Here, π and π are constant and r is the distance from the center. The volume charge density inside the ball is βπππ. The value of π is ______.
(π= permittivity of the medium)
(π= permittivity of the medium)
Correct Answer: 12
Solution and Explanation
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Concepts Used:
Electrostatics
Electrostatics is the branch of physics that deals with the study of stationary electric charges and their interactions. It involves the study of electric fields, electric charges, electric potential, and electric potential energy.
Electric charges are either positive or negative, and like charges repel while opposite charges attract. Electric charges can be generated by the transfer of electrons from one material to another, by contact between charged objects, or by induction, which involves the creation of an electric field that causes a separation of charges in a conductor.
Electric fields are regions in space around a charged object where an electric force is exerted on other charged objects. The strength of the electric field depends on the distance from the charged object and the magnitude of the charge.
Electric potential is a measure of the work required to move a unit charge from one point to another in an electric field. Electric potential energy is the energy that a charged object possesses due to its position in an electric field.
The behavior of electric charges and fields is described by Coulomb's law, which states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.
Electrostatics has numerous applications in technology, including in the design of electrical and electronic devices, such as capacitors and semiconductors. It also plays a vital role in everyday life, such as in the generation and distribution of electric power and in the functioning of the human nervous system.