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

Answer:

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?

Explanation:

Check attachment for solution

Answer 2

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

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 = $\frac{\epsilon*A}{d} *Ed =EA \epsilon$

But, A = πd²/4

Q = E(πd²/4)ε

$Q =\frac{E\pi d^2 \epsilon}{4} \\\\d^2 = \frac{4Q}{E\pi \epsilon} \\\\d =\sqrt{ \frac{4Q}{E\pi \epsilon}}$

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"

$d =\sqrt{ \frac{4Q}{E\pi \epsilon}} \\\\d =\sqrt{ \frac{4*3.36*10^{-10}}{1.6*10^5*\pi *8.854*10^{-12}}} \\\\d = 0.0174 \ m$

Therefore, the diameter of the disks is 0.0174 m