Electric Field and Electric Flux Calculation
What are the steps to calculate the electric field at the surface of the cylinder and the total electric flux through the cylinder?
Given a uniformly charged filament and an uncharged cardboard cylinder, how can we determine the electric field and electric flux using Gauss's law?
Calculation of Electric Field and Electric Flux:
To calculate the electric field at the surface of the cylinder, we first find the charge per unit length of the filament. This is done by dividing the total charge by the length of the filament. Using Gauss's law and the formula for electric flux via the cylinder, we can then determine the electric field and electric flux.
Given that we have a filament with a length of 4.95 m and a total positive charge of 2.00 µC, we can calculate the charge per unit length as follows:
Charge per unit length (λ) = Total charge / Length
Substitute the values:
λ = 2.00 µC / 4.95 m = 0.404 µC/m
Using Gauss's law and the formula for electric flux, we can now calculate the electric field at the surface of the cylinder:
Electric field (E) = λl' / (ε_o 2πrl')
Substitute the values and calculate:
E = (0.404 µC/m * 1.65 cm) / (8.85 x 10^-12 C^2/Nm^2 * 2 * 3.14 * 0.1 m * 0.0165 m) = 80.19 kN/C
Therefore, the electric field at the surface of the cylinder is 80.19 kN/C. To calculate the total electric flux through the cylinder, we use the formula:
Electric flux (ΦE) = λl' / ε_o
Substitute the values and calculate:
ΦE = (0.404 µC/m * 0.0165 m) / 8.85 x 10^-12 C^2/Nm^2 = 828.63 Nm^2/C
Thus, the total electric flux through the cylinder is 828.63 Nm^2/C.