Q65 / 75 · JEE Main 2026 (02 April Shift 2) · Physics
Two point charges $8 \, \mu C$ and $-2 \, \mu C$ are located at $x = 2$ cm and $x = 4$ cm, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii $3$ cm and $5$ cm with their centers at the origin is _______.
- A$4 : 1$
- B$3 : 4$
- Correct answerC$4 : 3$
- D$4 : 5$
Solution
According to Gauss's law, the electric flux through a closed surface is given by $\Phi = \dfrac{q_{\text{enclosed}}}{\varepsilon_0}$.
For the first sphere of radius $r_1 = 3$ cm centered at the origin, only the charge at $x = 2$ cm is enclosed.
$q_{\text{enclosed}, 1} = 8 \, \mu\text{C}$
$\Phi_1 = \dfrac{8 \, \mu\text{C}}{\varepsilon_0}$
For the second sphere of radius $r_2 = 5$ cm centered at the origin, both charges at $x = 2$ cm and $x = 4$ cm are enclosed.
$q_{\text{enclosed}, 2} = 8 \, \mu\text{C} - 2 \, \mu\text{C} = 6 \, \mu\text{C}$
$\Phi_2 = \dfrac{6 \, \mu\text{C}}{\varepsilon_0}$
The ratio of the electric flux is:
$\dfrac{\Phi_1}{\Phi_2} = \dfrac{8}{6} = \dfrac{4}{3}$
Answer: $4 : 3$
For the first sphere of radius $r_1 = 3$ cm centered at the origin, only the charge at $x = 2$ cm is enclosed.
$q_{\text{enclosed}, 1} = 8 \, \mu\text{C}$
$\Phi_1 = \dfrac{8 \, \mu\text{C}}{\varepsilon_0}$
For the second sphere of radius $r_2 = 5$ cm centered at the origin, both charges at $x = 2$ cm and $x = 4$ cm are enclosed.
$q_{\text{enclosed}, 2} = 8 \, \mu\text{C} - 2 \, \mu\text{C} = 6 \, \mu\text{C}$
$\Phi_2 = \dfrac{6 \, \mu\text{C}}{\varepsilon_0}$
The ratio of the electric flux is:
$\dfrac{\Phi_1}{\Phi_2} = \dfrac{8}{6} = \dfrac{4}{3}$
Answer: $4 : 3$
Hence, the correct answer is option: 'C'.