A uniform linear charge density of 4.0 nC/m is distributed along the entire x axis. Consider a spherical (radius = 5.0 cm) surface centered on the origin.Determine the electric flux through this surface.
Question
A uniform linear charge density of 4.0 nC/m is distributed along the entire x axis. Consider a spherical (radius = 5.0 cm) surface centered on the origin.Determine the electric flux through this surface.
Solution
The electric flux through a closed surface due to a charge distribution is given by Gauss's law:
Φ = Q_enclosed / ε_0
where Φ is the electric flux, Q_enclosed is the total charge enclosed by the surface, and ε_0 is the permittivity of free space.
In this case, the charge distribution is a uniform linear charge density along the x-axis. However, the spherical surface is centered on the origin, which means it does not enclose any of the charge distribution. Therefore, Q_enclosed = 0.
Substituting this into Gauss's law gives:
Φ = 0 / ε_0 = 0
So, the electric flux through the spherical surface is 0.
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