Understanding Electric Flux in a Cylinder with a Point Charge

What portion of the flux leaves the curved surface of the cylinder?

The given information states that a point charge is located at the center of a cylinder, and we need to determine the portion of the flux that leaves the curved surface of the cylinder.

Analysis

To solve this problem, let's consider the flux leaving the cylinder as a whole, denoted as Φ_total. According to the problem, the flux leaving one end of the cylinder is 20% of the total flux, which means Φ_end = 0.2 * Φ_total.

Since the point charge is located at the center of the cylinder, the electric field lines are symmetrical, and the flux leaving one end of the cylinder is equal to the flux leaving the other end. Therefore, the flux leaving the other end is also Φ_end = 0.2 * Φ_total.

Now, let's find the flux leaving the curved surface of the cylinder, denoted as Φ_curved. Since the flux leaving each end of the cylinder is 20% of the total flux, the remaining flux that leaves the curved surface is equal to the difference between the total flux and the flux leaving both ends:

Φ_curved = Φ_total - 2 * Φ_end.

Substituting the given values, we have:

Φ_curved = Φ_total - 2 * (0.2 * Φ_total) = Φ_total - 0.4 * Φ_total = 0.6 * Φ_total.

Therefore, the portion of the flux leaving the curved surface of the cylinder is 60% of the total flux.