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The electric field E is measured at a point P ( 0,0 , d ) , generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between E and d. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II. List

Options

  1. Aa-q,r;b-r,s;c-s,t;d-q,r;
  2. Ba-r;b-t;c-r;d-q,r,s,t;
  3. Ca-t;b-s;c-r,s,t;d-t;
  4. Da-t;b-r;c-p,s;d-q;

Correct answer

D. a-t;b-r;c-p,s;d-q;

Step-by-step solution

(i) Point charge E = K Q d 2 ⇒ E ∝ 1 d 2 ( i i ) Dipole E = 2 k p d 3 1 + 3 cos 2 ⁡ θ E ∝ 1 d 3 for dipole ( i i i ) For line charge E = 2 k λ d E ∝ 1 d (iv) Two line charge E = 2 k λ d - l - 2 K λ d + l = 2 K l d + l - d + l d 2 - l 2 E = 2 K λ 2 l d 2 1 - l 2 d 2 E ∝ 1 d 2 (v) Electric field due to sheet ∈ = σ 2 ∈ 0 ∈ = v is independent of r

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