An isolated charged conducting sphere of radius 10.0 cm creates an electric field of 4.90 104 N/C at a distance 23.0 cm from its center.
The concepts used to solve this problem are electric field due to conducting sphere, the surface area of the sphere, surface charge density and capacitance of the isolated spherical capacitor.
Use the expression of the electric field due to conducting sphere to calculate the charge on the sphere.
Use the expression for the surface area of the sphere to calculate the surface area of the sphere.
Use the expression of surface charge density to calculate the surface charge density of the sphere.
Use the expression for the capacitance of the isolated spherical capacitor to calculate the capacitance.
Write the expression for the electric field due to conducting sphere.
Here, is the electrostatic constant, is the charge on the conducting sphere and is the distance at which the electric field is evaluated from the center of the sphere.
Write the expression for the surface area of a sphere.
Here, is the radius of conducting sphere.
Write the expression for surface charge density.
Here, is the charge on the conducting sphere and is the surface area of the sphere.
Write the expression for the capacitance of the isolated spherical capacitor.
Here, is the absolute permittivity and is the radius of the sphere.
(a)
Calculate the charge on the sphere.
Write the expression for the electric field due to conducting sphere.
Here is the electrostatic constant, is the charge on the conducting sphere and is the distance at which the electric field is evaluated from the center of the sphere.
Rearrange for the charge.
Substitute for , for and for .
Calculate the area of the sphere.
Write the expression for surface area.
Here, is the radius of conducting sphere.
Substitute for .
Calculate the surface charge density on the sphere.
Write the expression for surface charge density.
Here, is the charge on the conducting sphere and is the surface area of the sphere.
Substitute for and for .
(b)
Write the expression for the capacitance of the isolated spherical capacitor.
Here, is the absolute permittivity and is the radius of the sphere.
Substitute for and for.
Ans: Part a
The surface charge density on the sphere is .
Part bThe capacitance of isolated sphere is .
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