Linear region : Note that this region of operation implies the existence of the uninterrupted channel between the source and the drain, which is ensured by the voltage relation VGS - Vth > VDS .
The voltage between the gate and the channel varies linearly with the distance x from the source due to the IR drop in the channel. Assume that the device is not saturated and the average channel voltage is VDS /2.
The effective gate voltage VG,eff = Vgs - Vth
Charge per unit area = 
where Eg average electric field from gate to channel, 
: relative permittivity of oxide between gate and channel
(~4.0 for SiO2 ), and
: free space permittivity (8.85 x 10 -14 F/cm).
So, induced charge 
.
where W: width of the gate and L : length of channel.
where D is the oxide thickness.
