Hi.
I was reading the Microelectronic Circuits be Sedra/Smith and I have some questions on Mosfets.
I will ask the questions one at a time.

On
4.1.3 Creating a Channel for Current Flow
"Consider next the situation depicted in Fig. 4.2. Here we have grounded the source and the drain and applied a positive voltage
to the gate. Since the source is grounded. the gate voltage appears in effect between gate and source and thus is denoted v_GS"



1st question: Does gate voltage also appears between gate and drain?

 

Yes. Since the potential difference between the source and the drain is zero, we know that even though the rds(on) of the n-channel is very small no current can flow.

 

Does gate voltage appears between gate and drain also?

By definition, if there's a voltage between the gate and source, then there has to be a voltage between gate and drain also.
Since MOSFETs are symmetrical, which terminal acts as the source is determined by the relative voltages on the 3 terminals, so a MOSFET can conduct equally well in either direction when biased on.
But for typical 3-terminal MOSFETs, the source terminal is the one that is connected to the substrate diode (terminal B) so that it is normally reverse-biased.