Match List I with List II
| LIST I | LIST II | ||
| A. | Electric field outside a uniformly charged thin spherical shell. | I. | zero |
| B. | Electric field inside the uniformly charged thin spherical shell | II. | \( \displaystyle\frac{\lambda}{2\pi\epsilon_0 r}\hat{n} \) |
| C. | Electric field due to an infinitely long straight uniformly charged wire. | III. | \( \displaystyle\frac{\sigma}{2\epsilon_0}\hat{n} \) |
| D. | Electric field due to a uniformly charged infinite plane sheet | IV. | \( k\displaystyle\frac{q}{r^{2}}\hat{r} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-IV, B-I, C-II, D-III
Each field follows from Gauss's law, \( \oint \vec{E}\cdot d\vec{A} = q_{\mathrm{enc}}/\epsilon_0 \), applied to a Gaussian surface that matches the symmetry of the charge.
(A) Electric field outside a uniformly charged thin spherical shell. — this matches (IV) \( k\displaystyle\frac{q}{r^{2}}\hat{r} \). A sphere of radius \( r \) outside the shell encloses the whole charge \( q \), so the shell acts as a point charge at its centre.
(B) Electric field inside the uniformly charged thin spherical shell — this matches (I) zero. A Gaussian sphere inside the shell encloses no charge, so the field is zero.
(C) Electric field due to an infinitely long straight uniformly charged wire. — this matches (II) \( \displaystyle\frac{\lambda}{2\pi\epsilon_0 r}\hat{n} \). A coaxial cylinder of radius \( r \) and length \( l \) encloses \( \lambda l \), and the flux \( E \cdot 2\pi r l \) passes only through its curved surface.
(D) Electric field due to a uniformly charged infinite plane sheet — this matches (III) \( \displaystyle\frac{\sigma}{2\epsilon_0}\hat{n} \). A pillbox of face area \( A \) encloses \( \sigma A \) and the flux leaves through both faces, \( 2EA \), so the field is the same at every distance.
NCERT (2026-27):
Summary – “… (i) Thin infinitely long straight wire of uniform linear charge density λ
\( \displaystyle \mathbf{E} = \frac{\lambda}{2\pi\varepsilon_0 r}\,\hat{\mathbf{n}} \)
… (ii) Infinite thin plane sheet of uniform surface charge density σ
\( \displaystyle \mathbf{E} = \frac{\sigma}{2\varepsilon_0}\,\hat{\mathbf{n}} \)
… (iii) Thin spherical shell of uniform surface charge density σ
\( \displaystyle \mathbf{E} = \frac{q}{4\pi\varepsilon_0 r^2}\,\hat{\mathbf{r}} \quad (r \geq R), \qquad \mathbf{E} = 0 \quad (r \lt R) \)
… 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.”