1
JEE Advanced 2018 Paper 2 Offline
+3
-0.75
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-$${\rm I}$$ contains different relations between $$E$$ and $$d$$. List-$${\rm II}$$ describes different electric charge distributions, along with their locations. Match the functions in List-$${\rm I}$$ with the related charge distributions in List-$${\rm II}$$.

LIST - I LIST - II
P. $$E$$ is independent of $$d$$ 1. A point charge Q at the origin
Q. $$E\, \propto \,1/d$$ 2. A small dipole with point charges
$$Q$$ at $$\left( {0,0,l} \right)$$ and $$-Q$$ at
$$\left( {0,0, - l} \right).$$ Take $$2l < < d$$
R. $$E\, \propto \,1/{d^2}$$ 3. An infinite line charge coincident
with the x-axis, with uniform linear charge density $$\lambda$$
S. $$E\, \propto \,1/{d^3}$$ 4. Two infinite wires carrying
uniform linear charge density
parallel to the $$x$$-axis. The one
along $$\left( {y = 0,z = l} \right)$$ has
a charge density $$+ \lambda$$ and the one
along $$\left( {y = 0,z = - l} \right)$$ has a
charge density Take
5. Infinite plane charge coincident
with the $$xy$$-plane with uniform surface charge density
A
$$P \to 5;Q \to 3,4;R \to 1;S \to 2$$
B
$$P \to 5;Q \to 3;R \to 1,4;S \to 2$$
C
$$P \to 4;Q \to 3;R \to 1,2;S \to 4$$
D
$$P \to 4;Q \to 2,3;R \to 1;S \to 5$$
2
JEE Advanced 2015 Paper 2 Offline
+4
-2
Consider a uniform spherical charge distribution of radius $${R_1}$$ centred at the origin $$O.$$ In this distribution, a spherical cavity of radius $${R_2},$$ centred at $$P$$ with distance $$OP=a$$ $$= {R_1} - {R_2}$$ (see figure) is made. If the electric field inside the cavity at position $$\overrightarrow r$$ is $$\overrightarrow E \overrightarrow {\left( r \right)} ,$$ then the correct statement(s) is (are) A
$$\overrightarrow E$$ is uniform, its magnitude is independent of $${R_2}$$ but its direction depends on $$\overrightarrow r .$$
B
$$\overrightarrow E$$ is uniform, its magnitude depends on $${R_2}$$ and its direction depends on $$\overrightarrow r .$$
C
$$\overrightarrow E$$ is uniform, its magnitude is independent of a but its direction depends on $$\overrightarrow a$$
D
$$\overrightarrow E$$ is uniform and both its magnitude and direction depend on $$\overrightarrow a$$
3
JEE Advanced 2014 Paper 2 Offline
+4
-1
Charges $$Q,$$ $$2Q$$ and $$4Q$$ are uniformly distributed in three dielectric solid spheres $$1,2$$ and $$3$$ of radii $$R/2,R$$ and $$2R$$ respectively, as shown in figure. If magnitude of the electric fields at point $$P$$ at a distance $$R$$ from the center of sphere $$1,2$$ and $$3$$ are $${E_1}$$, $${E_2}$$ and $${E_3}$$ respectively, then  A
$${E_1} > {E_2} > {E_3}$$
B
$${E_3} > {E_1} > {E_2}$$
C
$${E_2} > {E_1} > {E_3}$$
D
$${E_3} > {E_2} > {E_1}$$
4
JEE Advanced 2014 Paper 2 Offline
+3
-1

Four charges Q1, Q2, Q3 and Q4 of same magnitude are fixed along the x axis at x = $$-$$2a, $$-$$a, +a and +2a, respectively. A positive charge q is placed on the positive y axis 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$$_2$$, Q$$_3$$ negative 3. +y
S. Q$$_1$$, Q$$_3$$ positive; Q$$_2$$, Q$$_4$$ negative 4. $$-$$y

A
P-3, Q-1, R-4, S-2
B
P-4, Q-2, R-3, S-1
C
P-3, Q-1, R-2, S-4
D
P-4, Q-2, R-1, S-3
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