A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of $80.0 \, \mu ext{C/m}

Question

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of $80.0 \, \mu	ext{C/m}^2$. The charge on the sphere is:

Accepted Answer

The surface charge density $\sigma$ is defined as charge per unit area ($q/A$). For a sphere, the surface area is $A = 4\pi R^2$. 
Given:
Diameter $d = 2.4$ m $\Rightarrow$ Radius $R = 1.2$ m
Surface charge density $\sigma = 80.0 \, \mu	ext{C/m}^2 = 80.0 	imes 10^{-6}$ C/m$^2$

Calculation:
$q = \sigma 	imes 4\pi R^2$
$q = 80.0 	imes 10^{-6} 	imes 4 	imes 3.1416 	imes (1.2)^2$
$q = 80.0 	imes 10^{-6} 	imes 12.566 	imes 1.44$
$q \approx 1447.6 	imes 10^{-6}$ C
$q = 1.447 	imes 10^{-3}$ C.
(See NCERT Physics Class 12, Exercise 1.21).

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