Designing 60hz antenna to detect electric field
The wavelength of 60Hz is huge. In your convenient local-lab measurements, you will be in the "near field" where the Efield acts independent of the Hfield (magnetic field).

Simply dangling a wire from a 10Meg Ohm scope probe should get you volts of 60Hz. Bring the wire near the scope's powercord. Or near any light fixture. Set the scope to 20 or 50 milliSeconds per division; you should see huge spikes near an older-style non-electronic-ballast fluorescent light, as the arc is re-struck at 120 times per second; expect 200 volts in 10 microsecond risetime.

I was thinking, over the weekend, about volts/meter of field strength for 60 Hertz. Because of such nearness, volts/meter is impossible to measure to extract power.

What you have, and what I have in my Efield interference modeling, is simply capacitive coupling between 2 wires, or from a wire in your wall or power cord, to your sensing plate.

Grounding the "other plate" will shield the backside. In this case, you have two capacitors in series, forming a voltage divider. The Efield flux will still impinge on the side facing the power wiring.

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Lets model a coupling structure, of 2 wires that are 50 meters apart. Let each wire have 10cm diameter. The coupling capacitance is

EoErlength * 2*pi / ln(X * sqrt(X*X -1))

where that X is (separation ^2 - ... small terms) / (2*radius1*radius2)

and X is (50 * 50) / ( 2 * 5cm * 5cm)

X is 2,500 / (2 * 0.05 * 0.05) = 2,500*20*20/2

X is 500,000

natural_log (500,000 + 500,000) ~~ 2.3 * 6 = 14

The capacitance(per meter of receiver wire) is

~~ 50pF/meter / 14 = 3.5 picoFarad.

Technically, the mechanical topology is NOT 2 infinite wires, but one infinite (Power line) wire and your very short wire, thus more like the coupling between a wire and a small blob. 

But lets use the 3.5 picoFarad we have computed.
Why not? We are letting your receiver metal target be 10cm diam (5cm radius) and length 1meter.

I = C * dVdT = 3.5pF * 377rad/sec * 100,000 volts

I ~~ 1e-9 * 100,000 ~~ 1e-4 = 100uA

Across 10 Meg Ohm scope probe, expect 1e+7 * 1e-4 

or

1,000 volts.

So its dangerous to you and to the scope, to use large pieces of metal.