The electric field strength in the space between two closely spaced parallel disks is 1.0 × 10⁵ N/C. This field is the result of transferring 3.9 × 10⁹electrons from one disk to the other. What is the diameter of the disks? (e = 1.60 × 10^-19C, ε0 = 8.85 × 10^-12 C²/N ∙ m²)

Question

Quizplus · Accepted Answer

The electric field strength between the two disks can be calculated using the formula:

E = σ/2ε0

where σ is the surface charge density and ε0 is the electric permittivity of free space. Rearranging this formula gives:

σ = 2ε0E

The total charge transferred from one disk to the other can be found using the formula:

Q = ne

where n is the number of electrons transferred and e is the elementary charge. Substituting the given values, we have:

Q = (3.9 × 10^19) × (1.60 × 10^-19) = 6.24 × 10^0 C

The surface charge density can be obtained by dividing the total charge by the area of one of the disks:

σ = Q/A

The area of a disk is given by:

A = πr^2

where r is the radius of the disk. Substituting the given values, we have:

σ = (6.24 × 10^-1)/(πr^2)

Equating this expression for σ with the previous expression for σ, we get:

2ε0E = (6.24 × 10^-1)/(πr^2)

Solving for r, we get:

r = √[(6.24 × 10^-1)/(2ε0Eπ)] ≈ 1.5 cm

Therefore, the diameter of each disk is twice the radius, or 3.0 cm. Thus, the answer is A) 3.0 cm.

The Electric Field Strength in the Space Between Two Closely