m from the center of the disk.
We start by calculating the total charge on the disk using the formula: charge = charge_density * pi * radius²
Given that the charge density is 7.90 * 10⁻³ C/m² and the radius is 0.35 meters, our total charge on the disk comes out to be approximately 0.00304 C.
Next, we calculate the electric field on the axis of the disk at different distances using the formula: E = charge_density / (2 * epsilon_0) * (1 - distance / (r_squared ^ 0.5)), where epsilon_0 is the permittivity of free space (8.85 * 10⁻¹² F/m), and r_squared is the sum of radius² and distance².
For the first location, at a distance of 5.00 cm (or 0.05 meters), we calculate r_squared = 0.35² + 0.05² and substitute the values into the formula to get E ≈ 383207417.27 N/C.
Similarly, for the second location, at a distance of 10.0 cm (or 0.1 meters), we calculate r_squared = 0.35² + 0.1² and substitute the values into the formula to get E ≈ 323712038.96 N/C.
At the third location, at a distance of 50.0 cm (or 0.5 meters), we calculate r_squared = 0.35² + 0.5² and substitute the values into the formula to get E ≈ 80681798.186 N/C.
Lastly, at the fourth location, at a distance of 2 m, we calculate r_squared = 0.35² + 2², and substitute the values into the formula to get E ≈ 6681316.919 N/C.
So, to recap, the total charge on the disk is approximately 0.00304 C and the electric field on the axis of the disk at 5.00 cm, 10.0 cm, 50.0 cm, and 2 m are approximately 383207417.27 N/C, 323712038.96 N/C, 80681798.186 N/C, and 6681316.919 N/C, respectively.