Physics Q40 – JEE-MAIN 2026

Home Physics Electric Charges and FieldsQuestion #96

Two point charges

8 μ C

and

- 2 μ 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 _______.

Clue 1 of 3: Conceptual Principle

Gauss's Law states that the total electric flux through any closed surface is proportional to the net electric charge enclosed within that surface.

🧠 Full Solution Path

Step 1: Calculate flux through the first sphere✦ Active

The first sphere has a radius of $R_{1} = 3$ cm and is centered at the origin. The charges are $q_{1} = 8 μ C$ at $x = 2$ cm and $q_{2} = - 2 μ C$ at $x = 4$ cm.

Charge $q_{1}$ is at $x = 2$ cm, which is less than $R_{1} = 3$ cm, so $q_{1}$ is inside the sphere. Charge $q_{2}$ is at $x = 4$ cm, which is greater than $R_{1} = 3$ cm, so $q_{2}$ is outside the sphere.

According to Gauss's Law, the total charge enclosed by the first sphere is $Q_{e n c l o s e d, 1} = q_{1} = 8 μ C$ . The electric flux through the first sphere is:

Φ_{1} = \frac{Q_{e n c l o s e d, 1}}{ϵ_{0}} = \frac{8 μ C}{ϵ_{0}}

Step 2: Calculate flux through the second sphere○ Expand

The second sphere has a radius of $R_{2} = 5$ cm and is centered at the origin.

Charge $q_{1}$ is at $x = 2$ cm, which is less than $R_{2} = 5$ cm, so $q_{1}$ is inside the sphere. Charge $q_{2}$ is at $x = 4$ cm, which is less than $R_{2} = 5$ cm, so $q_{2}$ is also inside the sphere.

The total charge enclosed by the second sphere is $Q_{e n c l o s e d, 2} = q_{1} + q_{2} = 8 μ C + (- 2 μ C) = 6 μ C$ . The electric flux through the second sphere is:

Φ_{2} = \frac{Q_{e n c l o s e d, 2}}{ϵ_{0}} = \frac{6 μ C}{ϵ_{0}}

Step 3: Determine the ratio of electric fluxes○ Expand

The ratio of electric flux through the two spheres is:

\frac{Φ_{1}}{Φ_{2}} = \frac{\frac{8 μ C}{ϵ_{0}}}{\frac{6 μ C}{ϵ_{0}}} = \frac{8}{6} = \frac{4}{3}

The ratio is 4:3.

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Physics Question 40 – JEE-MAIN 2026

Clue 1 of 3: Conceptual Principle

🧠 Full Solution Path