Question

Two identical closely spaced circular disks form a parallel-plate capacitor. Transferring 2.1×109 electrons from one disk to the other causes the electric field strength between them to be 1.6×105 N/C .

Answer 1

Complete question:

Two identical closely spaced circular disks form a parallel-plate capacitor. Transferring 2.1 × 10⁹ electrons from one disk to the other causes the electric field strength between them to be 1.6 × 10⁵ N/C . What are the diameters of the disks ?

Answer:

The diameter of the disks is 0.0174 m

Step-by-step explanation:

Given;

charge, q on each sphere = 2.1 × 10⁹ x 1.6 x 10⁻¹⁹ C = 3.36 x 10⁻¹⁰ C

Electric field strength due to charged spheres, E = 1.6 × 10⁵ N/C

E = V/d

Capacitance is given as;

C = εA/d

The charge on a capacitor is given as;

Q = CV

Q =
`(\epsilon*A)/(d) *Ed =EA \epsilon`

But, A = πd²/4

Q = E(πd²/4)ε

`Q =(E\pi d^2 \epsilon)/(4) \\\\d^2 = (4Q)/(E\pi \epsilon) \\\\d =\sqrt{ (4Q)/(E\pi \epsilon)}`

where;

d is the diameter of the disks

ε is permittivity of free space = 8.854 x 10⁻¹² F/m

Substitute the given values and solve for "d"

`d =\sqrt{ (4Q)/(E\pi \epsilon)} \\\\d =\sqrt{ (4*3.36*10^(-10))/(1.6*10^5*\pi *8.854*10^(-12))} \\\\d = 0.0174 \ m`

Therefore, the diameter of the disks is 0.0174 m

Answer 2

Two identical closely spaced circular disks form a parallel-plate capacitor. Transferring 2.1×109 electrons from one disk to the other causes the electric field strength between them to be 1.6×105 N/C. What are the diameters of the disks?

Step-by-step explanation:

Check attachment for solution