Instruction manual

012-03175E
3
Measuring Charge
Charge measurement with the electrometer is indirect,
but simple. It is based on the relationship Q = CV,
where
Q and V are the charge and voltage across a capacitor
and C is the capacitance. The electrometer can be
thought of as an infinite impedance voltmeter in
parallel with a capacitor, as shown in Figure 2. The
capacitor represents the internal capacitance of the
electrometer, plus the capacitance of the leads.
When a charge is placed across the Electrometer leads,
a voltage V will read on the meter. If the value C is
known, the value of the charge can be calculated as
Q = CV. However, when you touch the Electrometer
leads to another object to test a charge, the capacitance
may change. If the object adds significant capacitance,
the situation becomes as shown in Figure 3. The new
capacitance (C + C
ext
) must be determined to accurately
calculate the charge from the measured voltage.
Measuring Charge by Induction
Under most conditions, the best way to measure charge
is by induction, using a proof plane and a Faraday ice
pail such as those included with PASCO’s Demonstra-
tion Electrostatics System. The proof plane is simply a
small conductive disk on an insulating handle. You
can make your own ice pail by mounting a conductive
cylinder on an insulating support, and placing a larger
conductive cylinder around it as a shield. Connect the
test lead of the electrometer probe to the inside cylin-
der, and connect the ground lead to the outside cylinder
(see Figure 4).
Volt-
meter
V
–Q
Q
C
Internal Capacitance of
Electrometer
(30-35 pf without Test
Probe; approximately
150 pf with Test Probe)
Q = CV
V
Q
–Q
Q'
–Q'
C
ext
C
Volt-
meter
Capacitance of object
connected to the
Electrometer
Figure 3 Change in Capacitance Due to
Charged Object
Q + Q' = (C + C
ext
) V
Figure 4 Using a Faraday Ice Pail
To sample the charge distribution on a charged object,
simply touch it with the proof plane, then place the
proof plane inside the inner cylinder of the ice pail,
without touching the cylinder. A charge is induced on
the inside cylinder that is equal but opposite to that on
the proof plane. You can now read the voltage on the
electrometer. By always using the proof plane and the
ice pail, the capacitance will be the same for all your
measurements and the charge on the proof plane will
always be proportional to the voltage reading of the
electrometer. However, in experiments for which you
want to know the absolute charge on the proof plane,
you need to know the total capacitance of the electrom-
eter, plus the test probe, plus the ice pail with the proof
plane inside it. Fortunately, this is easily measured, as
described below. Once you know the capacitance,
you can calculate the absolute charge for any measure-
ment as Q = CV.
Figure 2 Ideal Schematic of the Electrometer
Test lead
Electrometer
Ground lead
Faraday ice pail
Proof Plane