Question

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

• A. $\frac{2Q}{\varepsilon_0}$
• B. $\frac{5Q}{\varepsilon_0}$
• C. $\frac{7Q}{\varepsilon_0}$
• D. $\frac{3Q}{\varepsilon_0}$

Answer 1

Answer: (B)

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

Answer 2

Step 1: Analyze the Position of Charges Relative to the Sphere

A sphere of radius $4a$ centered at the origin includes the charge $5Q$ located at $(3a, 0)$ since $3a < 4a$. The charge $-2Q$ at $(-5a, 0)$ lies outside the sphere since $5a > 4a$.

Step 2: Apply Gauss’s Law

According to Gauss’s law, the electric flux $\Phi$ through a closed surface depends only on the net charge enclosed by the surface:

$\Phi = \frac{q_{\text{enc}}}{\varepsilon_0}$

Since only the $5Q$ charge is inside the sphere, the enclosed charge $q_{\text{enc}} = 5Q$.

Step 3: Calculate the Electric Flux

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

So, the correct answer is: $\frac{5Q}{\varepsilon_0}$