How do I assign a null value to a variable in PowerShell?

These are automatic variables, like $null, $true, $false etc.

about_Automatic_Variables, see https://technet.microsoft.com/en-us/library/hh847768.aspx?f=255&MSPPError=-2147217396

$NULL
$null is an automatic variable that contains a NULL or empty
value. You can use this variable to represent an absent or undefined
value in commands and scripts.

Windows PowerShell treats $null as an object with a value, that is, as
an explicit placeholder, so you can use $null to represent an empty
value in a series of values.

For example, when $null is included in a collection, it is counted as
one of the objects.

C:\PS> $a = ".dir", $null, ".pdf"
C:\PS> $a.count
3

If you pipe the $null variable to the ForEach-Object cmdlet, it
generates a value for $null, just as it does for the other objects.

PS C:\ps-test> ".dir", $null, ".pdf" | Foreach {"Hello"}
Hello
Hello
Hello

As a result, you cannot use $null to mean “no parameter value.” A
parameter value of $null overrides the default parameter value.

However, because Windows PowerShell treats the $null variable as a
placeholder, you can use it scripts like the following one, which
would not work if $null were ignored.

$calendar = @($null, $null, “Meeting”, $null, $null, “Team Lunch”, $null)
$days = Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"
$currentDay = 0

foreach($day in $calendar)
{
    if($day –ne $null)
    {
        "Appointment on $($days[$currentDay]): $day"
    }

    $currentDay++
}

output:

Appointment on Tuesday: Meeting
Appointment on Friday: Team lunch