%3Cp%3E%3Cstrong%3EA%20thin%26nbsp%3Bdisk%26nbsp%3Bof%26nbsp%3Buniform%26nbsp%3B
ID: 2274141 • Letter: #
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to calcualte the EF at point p a distance of z units from disk along the central axis.
our paln is to diide the disk into a very large no. of disks and then integrate them.
with r being radius and radial width being dr and let sigma be the charge per unit area
the chargeh on the ring is given by dq = sigma dA = sigma *(2pi r dr)
where dA is the differential area of the ring
EF due to ring og charge dq is given by dE = Z sigma ( 2pir) dr/( 4pie0 ( Z^2 +r^2)^3/2
dE = (sigma Z/4e0)*8( 2rdr/(Z^2+r^2)^3/2
now by integarting
E = int dE = (sigma Z/4e0) int ( Z^2+r^2)^-3/2 ffrom 0 to R
E = (sigma/4eo)* {(z^2+r^2)^-1/2} from 0 to R
E = (sigma/2e0){1-Z/sqrt(z^2+R^2)
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