The potential at the centre of a uniformly charged circular disc of radius 3 cm is 460V. What is the total charge on the disc?

Explanation

Data supplied,
V=460 volts `r=3 xx 10^(-2)m`
Potential (V) `=(sigma r)/(2epsi_(0))`
`sigma =(2epsi_(0)V)/(r)" But ",sigma=(q)/(pir^(2))`
`q/(pi r^(2))=(2epsi_(0)V)/(r)`
`q= (2pi epsi_(0) Vr)`
`=2 xx 3.14 xx 8.854 xx 10^(-12) xx 460 xx 3 xx 10^(-2)`
=0.7673nC

Surface charge density of disc `sigma(("say"))`
Consider a ring of radius x and thickness dx.
Charge of this ring `=2pi xdx sigma`
Potential at the centre due to this ring `=(1)/(4pi epsi_(0)) (2pi x sigma dx)/(x)=(sigma)/(2epsi_(0)) dx`
Whole disc (potential) `=sigma/(2epsi_(0)) underset(0)overset(x)int dx=(sigma)/(2epsi_(0)) r`