Question

Two circular disks spaced 0.50 mm apart form a parallel-plate capacitor. Transferring 1.70 x 10^9 electrons from one disk to the other causes the electric field strength to be 2.60 x 10^5 N/C.What are the daimeters of the disk?

Answer 1

The diameters of the disk is 1.23 cm

Step-by-step explanation:

Given information:

the space of two disks, d =0.5 mm = 0.0005 m = 5 x
`10^(-4)` m

the transferred electron, n = 1.70 x
`10^(9)`

electric field strength, E = 2.6 x
`10^(5)` N/C

to find the diameter of the disk we can use the following equation

A = πD²/4 ...........................................(1)

where

D = the distance of the disk

A = the area of the disk

first, we have to find the are of the disk using the capacitance equation

C = ε₀A/d...........................................(2)

A = Cd/ε₀ where C = Q/V (Q is total charge and V is potential difference)

thus

A = Qd/Vε₀.........................................(3)

now substitute V = Ed and Q = ne, so

A = (ned)/(Edε₀)

= ne/Eε₀..........................................(4)

e = 1.6 x
`10^(-19)` C

now can substitute equation (4) to the first equation

A = πD²/4

D² = 4A/π

D = √4A/π

= √(4ne)/(πEε₀) , ε₀ = 9.85 x
`10^(-12)` C²/Nm²

= √4(1.70 x
`10^(9)`)(1.6 x
`10^(-19)`)/π(2.6 x
`10^(5)` )(8.85 x
`10^(-12)` )

= 0.0123 m

= 1.23 cm