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Electrostatics question

2018 · Shift 2 · Q51
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Electrostatics question

2018 · Shift 2 · Q51

JEE AdvancedPhysicsElectrostaticsMCQ+3 / −0.75
The electric field EEE is measured at a point P(0,0,d)P(0,0,d)P(0,0,d) generated due to various charge distributions and the dependence of EEE on ddd is found to be different for different charge distributions. List-I{\rm I}I contains different relations between EEE and ddd. List-II{\rm II}II describes different electric charge distributions, along with their locations. Match the functions in List-I{\rm I}I with the related charge distributions in List-II{\rm II}II.

LIST - I LIST - II
P. EEE is independent of ddd 1. A point charge Q at the origin
Q. E ∝ 1/dE\, \propto \,1/dE∝1/d 2. A small dipole with point charges
QQQ at (0,0,l)\left( {0,0,l} \right)(0,0,l) and −Q-Q−Q at
(0,0,−l).\left( {0,0, - l} \right).(0,0,−l). Take 2l<<d2l \lt \lt d2l<<d
R. E ∝ 1/d2E\, \propto \,1/{d^2}E∝1/d2 3. An infinite line charge coincident
with the x-axis, with uniform linear charge density λ\lambdaλ
S. E ∝ 1/d3E\, \propto \,1/{d^3}E∝1/d3 4. Two infinite wires carrying
uniform linear charge density
parallel to the xxx-axis. The one
along (y=0,z=l)\left( {y = 0,z = l} \right)(y=0,z=l) has
a charge density +λ+ \lambda+λ and the one
along (y=0,z=−l)\left( {y = 0,z = - l} \right)(y=0,z=−l) has a
charge density Take
5. Infinite plane charge coincident
with the xyxyxy-plane with uniform surface charge density
  1. A
    P→5;Q→3,4;R→1;S→2P \to 5;Q \to 3,4;R \to 1;S \to 2P→5;Q→3,4;R→1;S→2
  2. B
    P→5;Q→3;R→1,4;S→2P \to 5;Q \to 3;R \to 1,4;S \to 2P→5;Q→3;R→1,4;S→2
  3. C
    P→4;Q→3;R→1,2;S→4P \to 4;Q \to 3;R \to 1,2;S \to 4P→4;Q→3;R→1,2;S→4
  4. D
    P→4;Q→2,3;R→1;S→5P \to 4;Q \to 2,3;R \to 1;S \to 5P→4;Q→2,3;R→1;S→5
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