To calculate the electric field on the axis of the disk at a distance of 5.00 cm from the center, we can use the formula for the electric field of a uniformly charged disk.
The electric field at a point on the axis of a uniformly charged disk is given by:
E = (σ / (2ε₀)) * (z / R^2 + z^2)^(-3/2)
where:
E is the electric field,
σ is the charge density of the disk (in C/m^2),
ε₀ is the permittivity of free space (ε₀ ≈ 8.854 × 10^-12 C^2/Nm^2),
z is the distance from the center of the disk to the point on the axis (in m),
R is the radius of the disk (in m).
Given values:
σ = 6.70 × 10^-3 C/m^2
z = 5.00 cm = 0.05 m
R = 35.0 cm = 0.35 m
Substituting these values into the formula, we get:
E = (6.70 × 10^-3 C/m^2 / (2 × 8.854 × 10^-12 C^2/Nm^2)) * (0.05 m / (0.35 m^2 + 0.05 m^2))^(-3/2)
Simplifying further, we have:
E = (6.70 × 10^-3 C/m^2 / (2 × 8.854 × 10^-12 C^2/Nm^2)) * (0.05 m / (0.36 m^2))^(-3/2)
Calculating the denominator:
E = (6.70 × 10^-3 C/m^2 / (2 × 8.854 × 10^-12 C^2/Nm^2)) * (0.05 m / 0.1296 m^2)^(-3/2)
Simplifying the exponent:
E = (6.70 × 10^-3 C/m^2 / (2 × 8.854 × 10^-12 C^2/Nm^2)) * (0.05 m / 0.0114 m^2)^(3/2)
Calculating the rightmost term:
E = (6.70 × 10^-3 C/m^2 / (2 × 8.854 × 10^-12 C^2/Nm^2)) * (0.05 m / 0.004125 m)
Finally, we calculate the electric field E:
E ≈ (6.70 × 10^-3 C/m^2 / (2 × 8.854 × 10^-12 C^2/Nm^2)) * 12.12 N/C
E ≈ 510.2 N/C
Therefore, the electric field on the axis of the disk at a distance of 5.00 cm from the center is approximately 510.2 N/C.