The net electric flux through a cubic box with sides that are 22.0 cm long is 4.90 × 10 3 N ⋅ m 2 / C 4.90×103 N⋅m2/C. What charge Q is enclosed by the box?

Respuesta :

Answer:

Q = 43.4 nC

Explanation:

According to the Gauss Law, the net electric flux through a closed surface, is equal to the charge enclosed by this surface, divided by the permitivitty of the free space, as follows:

Flux = Q/ε₀

If we know that the net electric flux through a cubic box with sides that are 22 cm. long, is 4.9*10³ N*m²/C, we can find the enclosed charge, defining a gaussian surface identical to this cube, as follows:

Qenc = 4.9*10³ N*m²/C * 8.85*10⁻¹² C²/N*m² = 43.4*10⁻⁹ C = 43.4 nC

The charge Q enclosed by the box is; Q_enc = 43.4 nC

How to find enclosed charge?

According to the Gauss Law, the formula for the net electric flux through a closed surface is;

Ф = Q/ε₀

where;

Ф is net electric flux

ε₀ = 8.85 × 10⁻¹² C²/N.m²

Q is charge

Now, since the net electric flux through a cubic box with sides that are 22 cm. long, is 4.9 × 10³ N.m²/C, it means that we can find the enclosed charge, defining a gaussian surface identical to this cube from:

Q_enc = 4.9 × 10³ N.m²/C 8.85 × 10⁻¹² C²/N*m²

Q_enc = 43.4 × 10⁻⁹ C

Q_enc = 43.4 nC

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