24. Electric Force & Field; Gauss' Law

Electric Flux

Multiple Choice
The electric flux through each surface of a cube is given below. Which surfaces of the cube does the electric field run parallel to?
Φ₁ = 100 Nm² /C      Φ₄ = 0 Nm² /C
Φ₂ = 20 Nm² /C       Φ₅ = −40 Nm² /C
Φ₃ = 0 Nm² /C        Φ₆ = −80 Nm² /C
Multiple Choice
Where does the normal vector point for a spherical shell?
Multiple Choice
What is the total flux through the two surfaces depicted in the following figure? Note that surface 1 has an area of 50 cm² and surface 2 has an area of 100 cm² , and E = 500 N/C.
Multiple Choice
A uniform electric field points in the positive x direction and has a magnitude of $40 N / C$ . What is the total flux through a rectangle with height $20 cm$ and width $45 cm$ ? The rectangle lies in the y-z plane.
Multiple Choice
A uniform electric field points in the positive x direction and has a magnitude of $40 N / C$ . What is the net flux through a cube with sides $4.0 cm$ ? The cube has one corner on the origin and the positive x, y, and z axes form three of its edges.
Multiple Choice
A cube has sides of $4.0 cm$ . Inside the cube is a $20 nC$ and a $- 30 nC$ charge. What is the net flux through the cube?
Multiple Choice
A $4.0 cm \times 5.0 cm$ rectangle lies in the x-y plane; let the normal vector point in the z direction. What is the flux through the rectangle of a uniform electric field $\overset{⇀}{E} = (- 7.8 \times 10^{5} \hat{j} + 2.3 \times 1 0^{5} \hat{k}) N / C$
Open Question
A hemispherical surface with radius r in a region of uniform electric field E→ has its axis aligned parallel to the direction of the field. Calculate the flux through the surface.
Open Question
A flat sheet of paper of area 0.250 m2 is oriented so that the normal to the sheet is at an angle of 60° to a uniform electric field of magnitude 14 N/C. (c) For what angle φ between the normal to the sheet and the electric field is the magnitude of the flux through the sheet (i) largest and (ii) smallest? Explain your answers.
Open Question
A flat sheet of paper of area 0.250 m2 is oriented so that the normal to the sheet is at an angle of 60° to a uniform electric field of magnitude 14 N/C. (a) Find the magnitude of the electric flux through the sheet. (b) Does the answer to part (a) depend on the shape of the sheet? Why or why not?
Open Question
A 2.0 cm×3.0 cm rectangle lies in the 𝓍𝒵-plane with unit vector nˆ pointing in the +y-direction. What is the electric flux through the rectangle if the electric field is(b) E (→ above E) = (4000 î−2000 kˆ) N/C?
Open Question
A 12 cm×12 cm rectangle lies in the first quadrant of the xy-plane with one corner at the origin. Unit vector nˆ points in the +𝒵 -direction. What is the electric flux through the rectangle if the electric field is E (→ above E) = (2000 m¯¹)x kˆ N/C?Hint: Divide the rectangle into narrow strips of width .
Open Question
A 10 nC charge is at the center of a 2.0 m x 2.0 m x 2.0 m cube. What is the electric flux through the top surface of the cube?
Open Question
The electric flux through the surface shown in FIGURE EX24.10 is 25 N m²/C . What is the electric field strength?
Open Question
Find the electric fluxes ΦA to ΦE through surfaces A to E in FIGURE P24.29.