Gauss's Law Applications

Question

A cubical Gaussian surface encloses a net charge of 8.85 nanocoulomb at its centre inside a vacuum, so what is the total electric flux through it?

RankGuru · Accepted Answer

Gauss's law states that the total electric flux through any closed surface equals the enclosed charge divided by the permittivity of free space, $\Phi = \frac{q_{enc}}{\varepsilon_0}$, as established in NCERT Class 12, Chapter 1 (Electric Charges and Fields). The flux depends only on the enclosed charge, not on the shape of the surface, so the cube geometry is irrelevant. Here $q_{enc} = 8.85	imes10^{-9}$ C and $\varepsilon_0 = 8.85	imes10^{-12}$ C²/N·m². Dividing gives $\Phi = \frac{8.85	imes10^{-9}}{8.85	imes10^{-12}} = 10^{3} = 1000$ N·m²/C. The value 500 N·m²/C is wrong because it incorrectly divides the flux by two, perhaps assuming only half the surface is pierced. The value 8.85 N·m²/C is wrong because it ignores the exponent difference between charge and permittivity entirely. The value 2000 N·m²/C is wrong because it doubles the correct result without basis. Note also that any charge lying outside the surface contributes zero net flux, since its field lines enter and leave the surface an equal number of times. A magnitude and sign check confirms positive enclosed charge gives positive outward flux, and the neat cancellation of the matching $8.85$ factors in charge and permittivity yields the clean $10^3$ result.

Gauss's Law Applications

Select the correct option:

🔒 Solution Hidden from View

More electrostatics Practice Questions

Using a long charged wire in a physics demonstration, the field around an infinite line charge follo...

Filling the gap of an air capacitor completely with a material of dielectric constant 4 changes its ...

Connecting two capacitors of 4 microfarad and 12 microfarad one after another in a series arrangemen...

Wiring the same 4 microfarad and 12 microfarad capacitors side by side in a parallel bank across one...

Charging a 10 microfarad capacitor in a camera flash circuit up to a potential of 200 volts stores e...

After disconnecting a charged isolated capacitor from its battery, the plate separation is doubled b...

Two protons are brought from very far apart to a separation of 1 femtometre inside a fusion reactor ...

Sketching the surfaces of constant potential around a single isolated positive point charge on a whi...

Once electrostatic equilibrium is reached inside a solid charged metallic conductor, the electric fi...

Inserting a dielectric slab of relative permittivity 5 between capacitor plates while the plates sta...

Moving a charge of 3 microcoulomb between two points raises its potential energy by changing potenti...

At a radial distance of 0.5 m from an isolated point charge of 5 nanocoulomb the potential takes a d...

About This Question

Solution