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JEE Advanced · Physics · 17. Electrostatics

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 -ILIST -II
A)is independent of dP)A point charge at the origin
B)\(E \propto \frac{1}{d}\)Q)A small dipole with point charges \(Q\) at \((0,0, l)\) and \(-\operatorname{Qat}(0,0, l)\). Take \(2 l \ll d\)
C)\(E \propto \frac{1}{d^2}\)R)An infinite line charge coincident with the \(x\)-axis, with uniform linear charge density \(\lambda\)
D)\(E \propto \frac{1}{d^3}\)S)Two infinite wires carrying uniform linear charge density parallel to the \(x\) - axis. The one along \((y-0, z=l)\) has a charge density \(+\lambda\) and the one along \((y=0, z=-l)\) has a charge density \(-\lambda\). Take \(2 l \ll d\)
T)Infinite plane charge coincident with the \(x y\) - plane with uniform surface charge density

  1. A a-q,r;b-r,s;c-s,t;d-q,r;
  2. B a-r;b-t;c-r;d-q,r,s,t;
  3. C a-t;b-s;c-r,s,t;d-t;
  4. D a-t;b-r;c-p,s;d-q;
Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

(i) Point charge
E=KQd2E1d2
(ii) Dipole
E=2kpd31+3cos2θ
E1d3 for dipole
(iii) For line charge
E=2kλd
E1d
(iv) Two line charge
E=2kλd-l-2Kλd+l
=  2Kld+l-d+ld2-l2
E=2Kλ2ld21-l2d2
E1d2
(v) Electric field due to sheet
=σ20
=v is independent of r
Same subject
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