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Calculate Field Issue/Script Setup Question

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I am attempting to add a new field to a feature class and then populate it based on a selection by attribute and then location. I originally setup this script to use CopyFeatures and it worked just fine. Instead, I would like to add the results to the new "Zoning" field I just created but do not know how to setup the expression in CalculateField.

Code:

# Import Arcpy
import arcpy

# Set the workspace
arcpy.env.workspace = "J:\\GIS\\Parcel_Data\\Python_Data\\For_Python_Script.gdb"

# Define Variables
fieldName1 = "Zoning"
fieldLength = "100"
Zoning_Designations = "Zoning_Designations"
CAMASUMMARY = "CAMASUMMARY"

# Define the feature class used below for adding the zoning field
fc = "J:\\GIS\\Parcel_Data\\Python_Data\\For_Python_Script.gdb\\CAMASUMMARY"

# Add the "Zoning" field to the parcel data
arcpy.AddField_management (fc, fieldName1, "TEXT", "", "", fieldLength)

# Select all parcels from CAMASUMMARY that match the zoning designations they encompass
flayer1 = arcpy.MakeFeatureLayer_management (Zoning_Designations, "Zoning_Layer")
flayer2 = arcpy.MakeFeatureLayer_management (CAMASUMMARY, "Parcel_Layer")
qry = '"name" = \'ARTS AND EDUCATION\''

arcpy.SelectLayerByAttribute_management (flayer1, "NEW_SELECTION", qry)
arcpy.SelectLayerByLocation_management (flayer2, "WITHIN", flayer1)
arcpy.CalculateField_management(CAMASUMMARY, fieldName1, ???????

Also, there will be 8 other queries exactly like this one (we have 9 zoning classifications) so can I just run one after the other? I think I need to clear the selection and delete the layers each time correct?

-Jonathan

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