Example of my etrade account: I have $3k cash and $0 margin debt and my account net balance shows $50k. I then sell to open a $4k position in XYZ how does this impact the cash, margin and net balance?
The FRB's RegT requires 150% of the value of the short sale. So if you short $4k of stock XYZ then you need $2k of cash in order to execute the trade. This is a more complicated way of saying that you need 50% of the value of the short position to open it. Brokers have the right to require a higher amount of margin.
The minimum required level of margin for the position is 25%. Again, brokers have the right to require a higher amount of margin. If you only had $2k in the account then for your short position, the minimum margin maintenance level would be $4,800.
With $3k in the account then you have additional buffer. Whether the remaining $47k of equity is marginable depends on what that equity is from (options with less than 9 months remaining until expiration and stocks under $5 are not marginable).