An empty, closed shoebox has a top and bottom that are 35.0 cm by 25.0 cm, verti

Question

An empty, closed shoebox has a top and bottom that are 35.0 cm by 25.0 cm, vertical sides that are 25.0 cm by 20.0 cm, and a front and back that are 20.0 cm by 35.0 cm. An external, uniform electric field of magnitude 6.00 × 103 N/C points 30º to the right of downward, as shown below (assume the electric field vector lies in the plane of the page, parallel to the front and back of the box). The box contains no electric charge. Important Note: Be sure to use the convention for surface normals, that they point outward from a closed surface. This will give negative flux for some sides of the surface.

Explanation / Answer

Electric flux through left vertical side = - 6.00 × 103*sin30 * 0.25 *0.20

                                                             = - 150 N .m2/C

Electric flux through right vertical side =    6.00 × 103*sin30 * 0.25 *0.20

                                                             =   150 N .m2/C

Electric flux through front side = 0 N .m2/C

Electric flux through back side = 0 N .m2/C

Electric flux through top side = - 6.00 × 103*cos30 * 0.35 *0.25

                                                = - 454.66 N .m2/C

Electric flux through bottom side =    6.00 × 103*cos30 * 0.35 *0.25

                                                =   454.66 N .m2/C

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