JEE Main 2026 — Apr 2, Shift 2 — Physics solution

JEE Main2026Apr 2, Shift 2Physics

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________.

A
$4 : 1$
B
$3 : 4$
C
$4 : 3$
D
$4 : 5$

Solution

By Gauss's law, only charges enclosed contribute to flux.

Sphere of radius $3$ cm (centred at origin) encloses only the $8 μ$ C charge at $x = 2$ cm: $ϕ_{1} = \frac{8 μ C}{ε _{0}}$ .

Sphere of radius $5$ cm encloses both charges: $ϕ_{2} = \frac{( 8 - 2 ) μ C}{ε _{0}} = \frac{6 μ C}{ε _{0}}$ .

$∴ \frac{ϕ _{1}}{ϕ _{2}} = \frac{8}{6} = \frac{4}{3}$ .

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