1
JEE Advanced 2023 Paper 2 Online
+3
-1
An electric dipole is formed by two charges $+q$ and $-q$ located in $x y$-plane at $(0,2) \mathrm{mm}$ and $(0,-2) \mathrm{mm}$, respectively, as shown in the figure. The electric potential at point $P(100,100) \mathrm{mm}$ due to the dipole is $V_0$. The charges $+q$ and $-q$ are then moved to the points $(-1,2) \mathrm{mm}$ and $(1,-2) \mathrm{mm}$, respectively. What is the value of electric potential at $P$ due to the new dipole? A
$\frac{V_0}{4}$
B
$\frac{V_0}{2}$
C
$\frac{V_0}{\sqrt{2}}$
D
$\frac{3 V_0}{4}$
2
JEE Advanced 2019 Paper 1 Offline
+3
-1 A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V0. A hole with a small area $$\alpha$$4$$\pi$$R2($$\alpha$$ << 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?
A
The ratio of the potential at the center of the shell of that of the point at $${1 \over 2}$$R from center towards the hole will be $${{1 - \alpha } \over {1 - 2\alpha }}$$.
B
The potential at the center of the shell is reduced by 2$$\alpha$$V0.
C
The magnitude of electric field at the center of the shell is reduced by $${{\alpha {V_0}} \over {2R}}$$.
D
The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance 2R from the center of the spherical shell will be reduced by $${{\alpha {V_0}} \over {2R}}$$.
3
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
$$P \to 4;Q \to 2,3;R \to 1;S \to 5$$
4
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 $$\overrightarrow a$$
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