A rectangular box (L = 30 cm, w = 26 cm, h = 10 cm) has a net charge q_encl encl

Question

A rectangular box (L = 30 cm, w = 26 cm, h = 10 cm) has a net charge q_encl enclosed Inside It. The figure below shows three electric fields, each pointing to the left, measured on the surface of the box. E_1 Is uniform over the right side of the box, E_2 Is uniform over the top, bottom, front, and back sides, and E_3 Is uniform over the left side. If the magnitudes of the electric fields are E_1 = 550 N/C, E_2 = 900 N/C, and E_3 = 1300 N/C, determine the value of q_encl. Note that the figure is not to scale. 0.0001898 times muC

Explanation / Answer

for upper, lower, back and front face,

E and A are perpendicular to each other.

flux = E.A = 0

for left side face:

flux1 = (w h ) E3 = ( 0.26 x 0.10 ) (1300) = 33.8 N m^2 / C

for right side face:

flux2 = - ( w h) (E1) = - 14.3 N m^2 / C

total flux = flux1 + flux2 = 19.5 N m^2 / C ..........Ans

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