Question 393: Electrostats & Capacitance

Question

Two charges of $$5 Q$$ and $$-2 Q$$ are situated at the points $$(3 a, 0)$$ and $$(-5 a, 0)$$ respectively. The electric flux through a sphere of radius '$$4 a$$' having center at origin is :

Accepted Answer

The electric flux through any closed surface is given by Gauss's law, which can be stated as:
$$ \Phi = \frac{Q_{	ext{enc}}}{\varepsilon_0} $$
where:
$$\Phi$$ = electric flux
$$Q_{	ext{enc}}$$ = total charge enclosed by the surface
$$\varepsilon_0$$ = permittivity of free space (electric constant)
In this scenario, we have a sphere of radius $$4a$$ with its center at the origin and two charges, $$5Q$$ at point (3a, 0) and $$-2Q$$ at point (-5a, 0). Since the sphere's radius is $$4a$$, the charge $$5Q$$, which is located at (3a, 0), lies inside the sphere, whereas the charge $$-2Q$$, located at (-5a, 0), lies outside the sphere. Gauss's law only considers charges that are enclosed within the surface.
Thus, the charge $$-2Q$$ has no impact on the electric flux through the sphere because it is not enclosed by the sphere. Only the charge $$5Q$$ contributes to the electric flux inside the sphere.
The electric flux through the sphere is therefore given simply by the enclosed charge:
$$ \Phi = \frac{5Q}{\varepsilon_0} $$

Answer

$$\frac{2 Q}{\varepsilon_0}$$

Answer

$$\frac{7 Q}{\varepsilon_0}$$

Answer

$$\frac{3 Q}{\varepsilon_0}$$

Answer

$$\frac{5 Q}{\varepsilon_0}$$

Electrostats & Capacitance

Two charges of $5 Q and -2 Q are situated at the points (3 a, 0) and (-5 a, 0) respectively. The electric flux through a sphere of radius '4 a$' having center at origin is :

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