A nonuniform electric field is directed along the x-axis at all points in space. This magnitude of the field varies with x, but not with respect to y or z. The axis of a cylindrical surface, 0.80 m long and 0.20 m in diameter, is aligned parallel to the x-axis. The electric fields E 1 and E 2, at the ends of the cylindrical surface, have magnitudes of 2000 N/C and 1000 N/C respectively, and are directed as shown. In Fig. 22.1, the charge enclosed by the cylindrical surface is closest to:

a. 0.28 nC
b. -0.60 nC
c. 1.2 nC
d. -1.2 nC
e. -0.28 nC

Complete question:

Check the image uploaded for the direction of the electric field, as indicated in Fig. 22.1.

(e) the charge enclosed by the cylindrical surface is closest to - 0.28 nC

Explanation:

Given;

length of the cylinder = 0.8 m

diameter of the cylinder = 0.2 m, radius, r = 0.1 m

electric field at the entering point of the cylinder, E₁ = 2000 N/C

electric field at the end point of the cylinder, E₂ = 1000 N/C

Total electric flux in the enclosed surface due to the parallel fields, is given as;

Φ = ΣE*A*cosθ

θ = 0, since the two fields are parallel to each other

Φ = ΣE*A = E₁A + E₂A

Flux through the entering point of the cylinder, E₁ is negative and positive at the end point, E₂ since no flux enter through this point.

Φ = ΣE*A =  -E₁A + E₂A

                = A( -E₁ + E₂)

                = πr²( -E₁ + E₂)

                = π(0.1)²( -2000 + 1000)

                = π(0.1)² ( -1000)

                = 0.03142 ( -1000)

                = -31.42 Nm²/C

Also,

Q enc. = Φ * ε₀

            = -31.42 *  8.85 x 10⁻¹²

            = - 0.278 x 10⁻⁹ C

            = - 0.28 nC

Thus, the charge enclosed by the cylindrical surface is closest to - 0.28 nC

do you have a formula possibly

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.