Match List-I with List-IIList-IList-II(Electric Field Intensity)(Char…

The correct answer is Option (2) → (A) - (II), (B) - (I), (C) - (IV), (D) - (III)

All four results follow from Gauss’s law.

(A) Electrical field intensity outside a uniformly charged thin spherical shell — this matches (II) Is inversely proportional to square of the distance. Outside, the shell acts as if all its charge were at the centre.

    \( \displaystyle E = \frac{1}{4\pi\varepsilon_0}\,\frac{q}{r^{2}} \)

(B) Electrical field intensity due to a uniformly charged infinite thin plane sheet — this matches (I) is constant. The field of an infinite sheet does not depend on the distance from the sheet.

    \( \displaystyle E = \frac{\sigma}{2\varepsilon_0} \)

(C) The electrical field intensity due to an infinitely long straight uniformly charged wire. — this matches (IV) Is inversely proportional to the distance. The field falls off as 1/r from the wire.

    \( \displaystyle E = \frac{\lambda}{2\pi\varepsilon_0 r} \)

(D) Electrical field intensity inside a charged spherical shell — this matches (III) is zero. A Gaussian surface inside the shell encloses no charge.

NCERT (2026-27):
Summary – “… 15. Gauss’s law: The flux of electric field through any closed surface S is 1/ε₀ times the total charge enclosed by S. The law is especially useful in determining electric field E, when the source distribution has simple symmetry:

(i) Thin infinitely long straight wire of uniform linear charge density \( \lambda \)

    \( \displaystyle \mathbf{E} = \frac{\lambda}{2\pi\varepsilon_0 r}\,\hat{\mathbf{n}} \)

where r is the perpendicular distance of the point from the wire and \( \hat{\mathbf{n}} \) is the radial unit vector in the plane normal to the wire passing through the point.

(ii) Infinite thin plane sheet of uniform surface charge density \( \sigma \)

    \( \displaystyle \mathbf{E} = \frac{\sigma}{2\varepsilon_0}\,\hat{\mathbf{n}} \)

where \( \hat{\mathbf{n}} \) is a unit vector normal to the plane, outward on either side.

(iii) Thin spherical shell of uniform surface charge density \( \sigma \)

    \( \displaystyle \mathbf{E} = \frac{q}{4\pi\varepsilon_0 r^2}\,\hat{\mathbf{r}} \quad (r \geq R) \qquad \mathbf{E} = 0 \quad (r \lt R) \)

where r is the distance of the point from the centre of the shell and R the radius of the shell. … The electric field outside the shell is as though the total charge is concentrated at the centre. … The field is zero at all points inside the shell.”