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 2016 Paper 2 Offline
+3
-0
Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now, a high voltage source (HV) connected across the conducting plates such that the bottom plate is at +V0 and the top plate at $$-$$V0. Due to their conducting surface, the balls will get charge, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)

Which one of the following statement is correct?
A
The balls will execute simple harmonic motion between the two plates
B
The balls will bounce back to the bottom plate carrying the same charge they went up with
C
The balls will stick to the top plate and remain there
D
The balls will bounce back to the bottom plate carrying the opposite charge they went up with
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