Question

Two 15-cm-diameter metal disks separated by a 0.69-mm-thick piece of Pyrex glass are charged to a potential difference of 1100 V .

What is the surface charge density on the disks?

What is the surface charge density on the glass?

Answer 1

here,

radius of Disk = 15/2 = 7.5cm = 0.075 m
Potential Difference = 1100 V
Thickness of Pyrex glass = t = .69mm = 0.00069 m

as,
C = (Epsilon)o * Area / (Distance between the plates)
C = Eo * A / D -----(1)

also We have
Charge = Capacitance * Potential Difference
Q = C * V-------------(2)

Therefore,
Q = Eo * A * V / D ---------(3)

Surface Charge density is given by,
Sigma = Charge / Area
From eqn4 we have,
Sigma = Eo * V / D -----------------(5)

Part A:

From Eqn 5,
Sigma = Eo * V / D
Sigma = 8.85*10^-12 * 1100 / 0.00069
Sigma = 1.41 * 10^-5 C/m^2

surface charge density on the disks is 1.41 * 10^-5 C/m^2

Part B :
as glass is between the plates so it act as Dielectric,so En5 can be rewritten as

Sigma = K * Eo * V / D --------------------(6)

Where K = 4.7 for Pyrex Glass

Therefore,
Sigma = 4.7 *8.85*10^-12 * 1100 / 0.00069
Sigma = 6.63*10^-5 C/m^2

the surface charge density on the glass is 6.63*10^-5 C/m^2