Question

Two 15-cm-diameter metal disks separated by a 0.59-mm-thick piece of Pyrex glass are charged to a potential difference of 1600 V .

A) What is the surface charge density on the disks?

η =   (in μC/m^2)

B) What is the surface charge density on the glass?

η (glass) = (in μC/m^2)

Answer 1

Part A.

We know that charge on capacitor plates is given by:

Q = C*V

Where C = capacitance of capacitor when dielectric is inserted between plates = k*e0*A/d

Q = k*e0*A*V/d

Now surface charge density on the disks will be given by:

= Q/A = (k*e0*A*V/d)/A

= k*e0*V/d

k = dielectric constant of Pyrex glass = 4.7

d = plate separation = 0.59 mm = 0.59*10^-3 m

Using known values:

= 4.7*8.854*10^-12*1600/(0.59*10^-3)

= 1.1285*10^-4 C/m^2 = 112.85*10^-6 C/m^2 = 112.85 C/m^2

In two significant figures (If you need)

= 110 C/m^2 = Surface charge density on the disks

Part B.

Now we need surface charge density on the glass, So first find the surface charge density on the disks when dielectric was not inserted, then subtract that from the surface charge density on disk when dielectric was inserted. So

Surface charge density on glass = when dielectric inserted - when there is no dielectric

1 = k*e0*V/d - e0*V/d

1 = (k - 1)*e0*V/d

1 = (4.7 - 1)*8.854*10^-12*1600/(0.59*10^-3)

1 = 8.884*10^-5 C/m^2 = 88.84*10^-6 C/m^2 = 88.84 C/m^2

In two significant figures

1 = 89 C/m^2

Let me know if you've any query.