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1

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)
Two charges, each equals to $$q,$$ are kept at $$x=-a$$ and $$x=a$$ on the $$x$$-axis. A particle of mass $$m$$ and charge $${q_0} = {q \over 2}$$ is placed at the origin. If charge $${q_0}$$ is given a small displacement $$\left( {y < < a} \right)$$ along the $$y$$-axis, the net force acting on the particle is proportional to
A
$$y$$
B
$$-y$$
C
$${1 \over y}$$
D
$$-{1 \over y}$$

Explanation



$$ \Rightarrow {F_{net}} = 2F\,\cos \theta $$

$${F_{net}} = {{2kq\left( {{q \over 2}} \right)} \over {{{\left( {\sqrt {{y^2} + {a^2}} } \right)}^2}}}.{y \over {\sqrt {{y^2} + {a^2}} }}$$

$${F_{net}} = {{2kq\left( {{q \over 2}} \right)y} \over {{{\left( {{y^2} + {a^2}} \right)}^{3/2}}}} \Rightarrow {{k{q^2}y} \over {{a^3}}}$$

S0, $$F \propto y$$
2

AIEEE 2012

MCQ (Single Correct Answer)
The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $$\tau $$ of this circuit lies between
A
100 sec and 150 sec
B
0 and 50 sec
C
50 sec and 100 sec
D
150 sec and 200 sec

Explanation

During discharging of a capacitor, V = V0$${e^{ - {t \over \tau }}}$$

At t = $$\tau $$,

V = $${{{V_0}} \over e}$$ = 0.37V0

From the graph, t = 0, V0 = 25 V

$$ \therefore $$ V = 0.37 $$ \times $$ 25 = 9.25 V

This voltage will occur at time between 100 sec and 150 sec. Hence, time constant $$\tau $$ of this circuit lies between 100 sec and 150 sec.
3

AIEEE 2012

MCQ (Single Correct Answer)
This question has statement- $$1$$ and statement- $$2.$$ Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $$R$$ has a uniformly positive charge density $$\rho $$. As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.

Statement- $$1:$$ When a charge $$q$$ is take from the centre of the surface of the sphere its potential energy changes by $${{q\rho } \over {3{\varepsilon _0}}}$$
Statement- $$2:$$ The electric field at a distance $$r\left( {r < R} \right)$$ from the center of the sphere is $${{\rho r} \over {3{\varepsilon _0}}}.$$

A
Statement- $$1$$ is true, Statement- $$2$$ is true; Statement- $$2$$ is not the correct explanation of Statement- $$1$$.
B
Statement $$1$$ is true, Statement $$2$$ is false.
C
Statement $$1$$ is false, Statement $$2$$ is true.
D
Statement- $$1$$ is true, Statement- $$2$$ is true; Statement- $$2$$ is the correct explanation of Statement- $$1$$.

Explanation

The electric field inside a uniformly charged sphere is

= $${{\rho .r} \over {3{ \in _0}}}$$

The electric potential inside a uniformly charged sphere

$$ = {{\rho {R^2}} \over {6{ \in _0}}}\left[ {3 - {{{r^2}} \over {{R^2}}}} \right]$$

$$\therefore$$ Potential difference between center and surface

$$ = {{\rho {R^2}} \over {6{ \in _0}}}\left[ {3 - 2} \right] = {{\rho {R^2}} \over {6{ \in _0}}}$$

$$\Delta U = {{q\rho {R^2}} \over {6{ \in _0}}}$$
4

AIEEE 2012

MCQ (Single Correct Answer)
In a uniformly charged sphere of total charge $$Q$$ and radius $$R,$$ the electric field $$E$$ is plotted as function of distance from the center. The graph which would correspond to the above will be:
A
B
C
D

Explanation

$${E_{in}} \propto r$$
$${E_{out}} \propto {1 \over {{r^2}}}$$

Questions Asked from Electrostatics

On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
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