Measure the dimensions of one of the parallel plates. It is not necessary to measure both plates as the plates are identical. For circular plates, measure the radius (r) of one of the plates. The radius is the distance from the center to the circumference of the plate. For rectangular plates, measure the width (W) and length (L) of one of the plates.
Calculate the surface area (A) of the parallel plates. Even though there are two identical plates, charge density only depends on the surface area of any one of these plates. The surface area depends on the shape of the plates. For circular plates, the surface area is: A = 3.14 x r^2. For example, if a circular parallel plate has a radius of 5 cm, the surface area of both plates is 78.5 cm^2 ([3.14 x (5^2)]^2). If the plates are rectangular, use the formula A = W x L. For example, if the rectangular plate has a length 10 cm and width 5 cm, then the surface area of the rectangular plate is 50 cm^2 ([5 x 10]^2).
Calculate the total charge (Q) on the parallel plates, using the formula Q = C x V. The unit for charge is the coulomb, with the symbol C. First measure the potential difference (V) across the plates using a voltmeter, and then multiply the potential difference by the capacitance (C) of the parallel plate structure to obtain the charge on the plates. While it can be determined empirically, it is recommended that you use the capacitance of the capacitor as supplied by the manufacturer of the device. The capacitance may be noted on the device itself and is identified by the unit farad or F. Be careful not to confuse the symbol for capacitance with the unit for charge. For example, if a parallel plate capacitor with a capacitance of 5 microfarad has a potential difference of 20 volts across the plates, then the charge stored on the plate is 1 x 10^-4 coulomb [(5 x 10^-6) x (20)].
Calculate the charge density on the parallel plates. The charge density equals (total charge) / (plate surface area) or Q/A. For example, if a rectangular parallel plate capacitor, with length 10 cm, width 5 cm, and capacitance 5 microfarad has a potential difference across the plates of 20 volts, then the charge density on the plates is: 2 x 10^-6 C/cm^2 = (1 x 10^-4 coulomb)/(50 cm ^2) = Q/A = (C x V) / (W x L).