 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2007

An electric charge ${10^{ - 3}}\,\,\mu \,C$ is placed at the origin $(0,0)$ of $X-Y$ co-ordinate system. Two points $A$ and $B$ are situated at $\left( {\sqrt 2 ,\sqrt 2 } \right)$ and $\left( {2,0} \right)$ respectively. The potential difference between the points $A$ and $B$ will be
A
$4.5$ volts
B
$9$ volts
C
zero
D
$2$ volts

Explanation The distance of point $A\left( {\sqrt 2 ,\sqrt 2 } \right)$ from the origin,

$OA = \left| {\overrightarrow {{r_1}} } \right|$

$= \sqrt {{{\left( {\sqrt 2 } \right)}^2} + {{\left( {\sqrt 2 } \right)}^2}}$

$= \sqrt 4 = 2$

The distance of point $B(2,0)$ from the origin,

$OB = \left| {\overrightarrow {{r_2}} } \right| = \sqrt {{{\left( 2 \right)}^2} + {{\left( 0 \right)}^2}} = 2$ units.

Now, potential at $A,$ ${V_A} = {1 \over {4\pi { \in _0}}}.{Q \over {\left( {OA} \right)}}$

Potential at $B,$ ${V_B} = {1 \over {4\pi { \in _0}}}.{Q \over {\left( {Ob} \right)}}$

$\therefore$ Potential difference between the points $A$ and $B$ is zero.
2

AIEEE 2006

Two insulating plates are both uniformly charged in such a way that the potential difference between them is ${V_2} - {V_1} = 20\,V.$ (i.e., plate $2$ is at a higher potential). The plates are separated by $d=0.1$ $m$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1.$ What is its speed when it hits plate $2$?
$\left( {e = 1.6 \times {{10}^{ - 19}}\,C,\,\,{m_e} = 9.11 \times {{10}^{ - 31}}\,kg} \right)$ A
$2.65 \times {10^6}\,m/s$
B
$7.02 \times {10^{12}}\,m/s$
C
$1.87 \times {10^6}\,m/s$
D
$32 \times {10^{ - 19}}\,m/s$

Explanation

$eV = {1 \over 2}m{v^2}$

$\Rightarrow v = \sqrt {{{2ev} \over m}} = \sqrt {{{2 \times 1.6 \times {{10}^{ - 19}} \times 20} \over {9.31 \times {{10}^{ - 31}}}}}$

$= 2.65 \times {10^6}\,m/s$
3

AIEEE 2006

Two spherical conductors $A$ and $B$ of radii $1$ $mm$ and $2$ $mm$ are separated by a distance of $5$ $cm$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is
A
$4:1$
B
$1:2$
C
$2:1$
D
$1:4$

Explanation After connection, ${V_1} = {V_2}$

$\Rightarrow K{{{Q_1}} \over {{r_1}}} = K{{{Q_2}} \over {{r^2}}}$

$\Rightarrow {{Q{}_1} \over {{r_1}}} = {{{Q_2}} \over {{r_2}}}$

The ratio of electric fields

${{{E_1}} \over {{E_2}}} = {{K{{{Q_1}} \over {r_1^2}}} \over {K{{{Q_2}} \over {r_2^2}}}} = {{{Q_1}} \over {r_1^2}} \times {{r_2^2} \over {{Q_2}}}$

$\Rightarrow {{{E_1}} \over {{E_2}}} = {{{r_1} \times r_2^2} \over {r_1^2 \times {r_2}}} \Rightarrow {{{E_1}} \over {{E_2}}} = {{{r_2}} \over {{r_1}}} = {2 \over 1}$

Since the distance between the spheres is large as compared to their diameters, the induced effects may be ignored.
4

AIEEE 2006

An electric dipole is placed at an angle of ${30^ \circ }$ to a non-uniform electric field. The dipole will experience
A
a translation force only in the direction of the field
B
a translation force only in a direction normal to the direction of the field
C
a torque as well as a translational force
D
a torque only

Explanation The electric field will be different at the location of the two charges. Therefore the two forces will be unequal. This will result in a force as well as torque.