A point charge is placed at the center of a net uncharged spherical conducting shell of inner radius 2.5 cm and outer radius 4.0 cm. As a result, the outer surface of the shell acquires a surface charge density σ = 71nC/cm2. Find (a) the value of the point charge, and (b) the surface charge density on the inner wall of the shell. Q = σA
Surface area of a sphere is 4 pi r^2.
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To solve this problem, we will use Gauss's law for electrostatics, which states that the electric flux through a closed surface is proportional to the charge enclosed by that surface.
(a) To find the value of the point charge, we need to consider the closed surface inside the shell. This enclosed surface is the inner surface of the conducting shell.
The electric flux through this closed surface is zero because the shell is net uncharged. Hence, the charge enclosed within the closed surface must also be zero.
Therefore, the value of the point charge is zero.
(b) To find the surface charge density on the inner wall of the shell, we need to consider the closed surface enclosing the point charge and the inner surface of the conducting shell.
The electric flux through this closed surface is proportional to the charge enclosed within it. In this case, the enclosed charge is the point charge at the center of the shell.
Since the point charge is zero, the electric flux through the closed surface is zero. However, the outer surface of the shell acquires a surface charge density σ = 71nC/cm^2.
Since the inner surface must acquire the same amount of charge of opposite sign to the outer surface, the surface charge density on the inner wall of the shell is also σ = 71nC/cm^2.