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

The Correct Option is B

Step 1: Determine Charge Location Relative to Sphere

The sphere has a radius of \(4a\) and is centered at the origin. The charge \(5Q\) is located at \((3a, 0)\), which is inside the sphere because \(3a<4a\). The charge \(-2Q\) is at \((-5a, 0)\), which is outside the sphere because \(5a>4a\).

Step 2: Apply Gauss’s Law

Gauss's law states that the electric flux \(\Phi\) through a closed surface is proportional to the net charge enclosed by that surface:

\[ \Phi = \frac{q_{\text{enc}}}{\varepsilon_0} \]

Only the \(5Q\) charge is enclosed by the sphere. Therefore, the enclosed charge is \(q_{\text{enc}} = 5Q\).

Step 3: Calculate Electric Flux

\[ \Phi = \frac{5Q}{\varepsilon_0} \]

The electric flux is: \(\frac{5Q}{\varepsilon_0}\)