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The electric flux through each of the six sides of a rectangular box is as follows:

[tex]\[
\Phi_1 = 143.6 \, N \cdot m^2 / C, \quad \Phi_2 = 266.0 \, N \cdot m^2 / C, \quad \Phi_3 = -342.5 \, N \cdot m^2 / C, \quad \Phi_4 = 191.1 \, N \cdot m^2 / C, \quad \Phi_5 = -119.5 \, N \cdot m^2 / C, \quad \Phi_6 = 453.4 \, N \cdot m^2 / C
\][/tex]



Answer :

GinnyAnswer
To find the total electric flux through the rectangular box, you need to sum the electric fluxes through the six sides of the box. Here is the step-by-step process:

1. Identify the given electric fluxes:
[tex]\[ \Phi_1 = 143.6 \, \text{N} \cdot \text{m}^2 / \text{C} \][/tex]
[tex]\[ \Phi_2 = 266.0 \, \text{N} \cdot \text{m}^2 / \text{C} \][/tex]
[tex]\[ \Phi_3 = -342.5 \, \text{N} \cdot \text{m}^2 / \text{C} \][/tex]
[tex]\[ \Phi_4 = 191.1 \, \text{N} \cdot \text{m}^2 / \text{C} \][/tex]
[tex]\[ \Phi_5 = -119.5 \, \text{N} \cdot \text{m}^2 / \text{C} \][/tex]
[tex]\[ \Phi_6 = 453.4 \, \text{N} \cdot \text{m}^2 / \text{C} \][/tex]

2. Sum all the electric fluxes:
[tex]\[ \text{Total Flux} = \Phi_1 + \Phi_2 + \Phi_3 + \Phi_4 + \Phi_5 + \Phi_6 \][/tex]

3. Write down the addition of each flux term:
[tex]\[ \text{Total Flux} = 143.6 + 266.0 + (-342.5) + 191.1 + (-119.5) + 453.4 \][/tex]

4. Combine the positive flux values:
[tex]\[ 143.6 + 266.0 + 191.1 + 453.4 = 1054.1 \][/tex]

5. Combine the negative flux values:
[tex]\[ -342.5 + (-119.5) = -462.0 \][/tex]

6. Add the combined positive and negative results:
[tex]\[ 1054.1 + (-462.0) = 592.1 \][/tex]

Therefore, the total electric flux through the rectangular box is:
[tex]\[ \boxed{592.1 \, \text{N} \cdot \text{m}^2 / \text{C}} \][/tex]

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