Electric Charges and Fields
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. ListI contains different relations between E and d. ListII describes different electric charge distributions, along with their locations. Match the functions in ListI with the related charge distributions in ListII.
LIST–I  LIST–II  
P.  E is independent of d  1.  A point charge Q at the origin 
Q.  $E\propto \frac{1}{d}$  2.  A small dipole with point charges Q at (0, 0, l) and –Q at (0, 0, –l). Take 2l ≪ d 
R.  $E\propto \frac{1}{{d}^{2}}$  3.  An infinite line charge coincident with the xaxis, with uniform linear charge density λ 
S.  $E\propto \frac{1}{{d}^{3}}$  4.  Two infinite wires carrying uniform linear charge density parallel to the x axis. The one along (y = 0, z = l) has a charge density +λ and the one along (y = 0, z = –l) has a charge density –λ. Take 2l ≪ d 
5.  Infinite plane charge coincident with the xyplane with uniform surface charge density 
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JEE Advanced 2018
Four charges Q_{1}, Q_{2}, Q_{3} and Q_{4} of same magnitude are fixed along the xaxis at x = −2a, −a, +a and +2a, respectively. A positive charge q is placed on the positive yaxis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists.
List I  List II  
P.  Q_{1}, Q_{2}, Q_{3}, Q_{4} all positive  1.  +x 
Q.  Q_{1}, Q_{2} positive; Q_{3}, Q_{4} negative  2.  −x 
R.  Q_{1}, Q_{4} positive; Q_{2}, Q3 negative  3.  +y 
S.  Q_{1}, Q_{3} positive; Q_{2}, Q_{4} negative  4.  −y 
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JEE Advanced 2014
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JEE Advanced 2012
The axis of a hollow cone as shown in the figure. It is kept in a uniform electric field E parallel to its axis (Take h = 10 m and R = 2m)
Column I  Column II  
1)  Magnitude of Flux through the base of the cone  a)  Non Zero 
2)  Magnitude of Flux through the curved part of the cone  b)  Zero 
3)  Magnitude of Flux through curved part of ABDC  c)  2πE 
4)  Net Flux through the entire cone  d)  4πE 
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JEE Advanced 0
In the ListI, some metallic objects are shown and the direction of current through them is shown by arrow(s). ListII contains the resistances. Assuming ρ to be density of material of each of the given object , match ListI with ListII
ListI  ListII  
(P) 

(1)  $\frac{\rho c}{\mathrm{\pi}\left({a}^{2}{b}^{2}\right)}$ 
(Q) 

(2)  $\frac{\rho}{4\mathrm{\pi}}\left(\frac{ab}{ab}\right)$ 
(R) 
A hollow cylinder with inner and outer radius b and a respectively 
(3)  $\frac{\rho c}{\mathrm{\pi}ab}$ 
(S) 

(4)  $\frac{\rho}{2\mathrm{\pi c}}\mathrm{ln}\left(\frac{a}{b}\right)$ 
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JEE Mains 0
In ListI, the charged objects are given, ListII contains the nature of electric field at point P inside the charged object.
Match the ListI with ListII
Match the ListI with ListII
ListI  ListII  
(P)  object→ uniformly charged spherical shell with centre at O 
(1)  Zero 
(Q)  object→ uniformly charged hollow cylinder (infinite length) 
(2)  uniform 
(R) 

(3)  Parallel to $\overrightarrow{a}$ 
(S)  object→ uniformly charged solid cylinder (infinite length) 
(4)  Nonuniform 
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JEE Mains 0