JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Electrostatics

A point charge causes an electric flux of

- 2 \times 1 0^{4} Nm^{2} C^{- 1}

to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :

(Given

ϵ_{0} = 8.85 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}

)

Answer: (A)

Solution

By Gauss's law, the flux through a closed surface depends only on the enclosed charge:

ϕ = \frac{q}{ϵ _{0}} ⟹ q = ϵ_{0} ϕ

q = (8.85 \times 1 0^{- 12}) \times (- 2 \times 1 0^{4}) = - 17.7 \times 1 0^{- 8} C

The 8.0 cm radius of the Gaussian surface plays no role in the result, since flux through any closed surface enclosing the same charge is the same.

JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Single correct option