A charge Q is located inside a rectangular box. The electric flux through each of the six surfaces of the box is: Ö1 = +1480 N · m2/C, Ö2 = +2240 N · m2/C, Ö3 = +4220 N · m2/C, Ö4 = -1780 N · m2/C, Ö5 = -3550 N · m2/C, and Ö6 = -5250 N · m2/C. What is Q?
add up all the flux
then use Gauss law
total flux out = charge inside/eo
where eo = 8.854 *10^-12 coulombs^2/Nm^2
To find the charge Q located inside the rectangular box, we can use Gauss's Law, which states that the total electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space (ε₀).
In this case, since the charge Q is located inside the box, the total electric flux through the six surfaces of the box should be equal to the flux due to the charge Q enclosed by these surfaces.
Let's consider each surface of the box individually:
Surface Ö1: The electric flux is given as +1480 N · m²/C. Since this flux has a positive sign, it indicates that the field lines are leaving the surface. Therefore, we can conclude that there is no charge enclosed by this surface (Q = 0).
Surface Ö2: The electric flux is given as +2240 N · m²/C. Similarly, since the flux has a positive sign, there is no charge enclosed by this surface (Q = 0).
Surface Ö3: The electric flux is given as +4220 N · m²/C. Again, this positive flux suggests that no charge is enclosed by this surface (Q = 0).
Surface Ö4: The electric flux is given as -1780 N · m²/C. Since this flux has a negative sign, it indicates that the field lines are entering the surface. Therefore, there must be a negative charge enclosed by this surface.
Surface Ö5: The electric flux is given as -3550 N · m²/C. Similarly, since the flux has a negative sign, there must be a negative charge enclosed by this surface.
Surface Ö6: The electric flux is given as -5250 N · m²/C. Again, this negative flux suggests that there must be a negative charge enclosed by this surface.
In summary, surfaces Ö1, Ö2, and Ö3 have no charge enclosed (Q = 0), while surfaces Ö4, Ö5, and Ö6 have negative charges enclosed.
Therefore, we need to determine the total negative charge enclosed by surfaces Ö4, Ö5, and Ö6. To find this charge, we can sum the absolute values of the electric fluxes: |Ö4| + |Ö5| + |Ö6|.
|Ö4| = |-1780 N · m²/C| = 1780 N · m²/C
|Ö5| = |-3550 N · m²/C| = 3550 N · m²/C
|Ö6| = |-5250 N · m²/C| = 5250 N · m²/C
Total negative charge (|Q|) = |Ö4| + |Ö5| + |Ö6| = 1780 N · m²/C + 3550 N · m²/C + 5250 N · m²/C.
Calculating the sum, we get:
Total negative charge (|Q|) = 10580 N · m²/C
Finally, since the charges enclosed by surfaces Ö4, Ö5, and Ö6 are negative, we can conclude that the charge inside the rectangular box is Q = -10580 C.