A empty cardboard box is placed in an electric field pointing upwards with a str

Question

A empty cardboard box is placed in an electric field pointing upwards with a strength of 1800 N/C as shown above. The bottom of the box is tilted up by an angle ? = 14o from the horizontal. Side A of the box faces out of the page and is 11 cm high and 13 cm long. Sides B and C are 11 cm high and 10 cm deep. Sides D and E are 13 cm long and 10 cm deep.

1) What is the flux through side A of the box? ?A = _____ N m2C

2) What is the flux through side B of the box? ?B = _____ N m2C

3) What is the flux through side C of the box? ?C = _____ N m2C

4) What is the flux through side D of the box? ?D = _____ N m2C

5) What is the flux through side E of the box? ?E = _____ N m2C

6) What is the total flux through all six sides of the box? ?Total = _____ N m2C

Explanation / Answer

Resolve field directions into x and y components : Ecos and E sin

1) The flux through side A is

A = EA cos = 0 N -m2-C because the the electric lines of forces are perpendicular to the surface A, the = 90 deg .

2) The flux through side B is

B = - E A sin = - (1800) (0.011 x 0.010) sin14 = - 0.0479 N -m2-C

3) The flux through side C is

C = - E A sin = (1800) (0.011 x 0.010) sin14 = 0.0479 N -m2-C

4) The flux through side D is

D = - E A cos = (1800) (0.013 x 0.010) cos14 = 0.2270 N -m2-C

5) The flux through side E is

D = - E A cos = - (1800) (0.013 x 0.010) cos14 = - 0.2270 N -m2-C

6) Therefore the net flux through all the sides is  Total = ___0__ N -m2-C

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