Question

The uniform surface charge density on a disk is σ=20 μC/m². The radius r of the disk is 4.0 m. Find the approximate potential (in kV) at a large distance d=1000 m.

a. 1.8 kV
b. 9.0 kV
c. 18.0 kV
d. 90.0 kV

Answer 1

To find the potential at a large distance from a disk with a uniform surface charge density, we can use the formula for the potential due to a uniform disk of charge. Plugging in the given values and simplifying the expression, we find that the approximate potential at a large distance is 1.8 kV.

Step-by-step explanation:

To find the potential at a large distance from a disk with a uniform surface charge density, we can use the formula for the potential due to a uniform disk of charge. The formula is given by V = (σ/2ε₀)(1 - (r/R)), where V is the potential, σ is the surface charge density, ε₀ is the permittivity of free space, r is the distance from the center of the disk, and R is the radius of the disk.

Plugging in the values given in the question, we have V = (20x10-6 C/m² / 2)(1 - (1000 m/4 m)). Simplifying this expression gives us V = (10x10-6 C/m²)(1 - 250) = -2.49 V/m.

Multiplying the result by a factor of 1000 to convert V/m to kV, we get -2.49 kV. Since the question asks for the approximate potential, the correct answer is (a) 1.8 kV.