In a certain region of space, the electric field is constant in direction (say horizontal, in the x direction), but its magnitude decreases from E = 560 N/C at x = 0 to E = 410 N/C at x = 25 m. Determine the charge within a cubical box of side l = 25 m, where the box is oriented so that four of its sides are parallel to the field lines.

Question

Physics

Trace Mccullough

22 October, 23:49

In a certain region of space, the electric field is constant in direction (say horizontal, in the x direction), but its magnitude decreases from E = 560 N/C at x = 0 to E = 410 N/C at x = 25 m. Determine the charge within a cubical box of side l = 25 m, where the box is oriented so that four of its sides are parallel to the field lines.

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Answers (1)

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Haney · Answer 1

8.3 x 10⁻⁷ C

Explanation:

Electric flux will enter the face at x=0 and exit at face x = 25 m

On the other faces, field lines are parallel so no flux will enter or exit.

Flux entering the face at x = 0

= electric field x face area

= 560 x 25 x 25 = 350000 weber

Flux exiting the face at x = 25

= 410 x 25 x25

= 256250 weber

Net flux exiting from cube (closed face)

350000 - 256250 = 93750 web

Apply gauss'es theorem

Q / ε = Flux coming out

Q is charge inside the closed cube

Q / ε = 93750

Q = 8.85 x 10⁻¹² x 93750

= 8.3 x 10⁻⁷ C