JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2005

Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+q$ and $-q.$ The potential difference between the centres of the two rings is
A
${q \over {2\pi \,{ \in _0}}}\left[ {{1 \over R} - {1 \over {\sqrt {{R^2} + {d^2}} }}} \right]$
B
${{qR} \over {4\pi \,{ \in _0}\,{d^2}}}$
C
${q \over {4\pi \,{ \in _0}}}\left[ {{1 \over R} - {1 \over {\sqrt {{R^2} + {d^2}} }}} \right]$
D
zero

Explanation

${V_A} = {V_{self}} + {V_{due}}$ to $(2)$

$\Rightarrow {V_A} = {1 \over {4\pi {\varepsilon _0}}}\left[ {{q \over R} - {q \over {\sqrt {{R^2} + {d^2}} }}} \right]$

${V_B} = {V_{self}} + {V_{due}}$ to $(1)$

$\Rightarrow {V_B} = {1 \over {4\pi {\varepsilon _0}}}\left[ {{{ - q} \over R} + {q \over {\sqrt {{R^2} + {d^2}} }}} \right]$

$\Delta V = {V_A} - {V_B}$
$= {1 \over {4\pi {\varepsilon _0}}}\left[ {{q \over R} + {q \over R} - {q \over {\sqrt {{R^2} + {d^2}} }} - {q \over {\sqrt {{R^2} + {d^2}} }}} \right]$

$= {1 \over {2\pi {\varepsilon _0}}}\left[ {{q \over R} - {q \over {\sqrt {{R^2} + {d^2}} }}} \right]$
2

AIEEE 2005

Two point charges $+8q$ and $-2q$ are located at $x=0$ and $x=L$ respectively. The location of a point on the $x$ axis at which the net electric field due to these two point charges is zero is
A
${L \over 4}$
B
$2$ $L$
C
$4$ $L$
D
$8$ $L$

Explanation

${{ - K2q} \over {{{\left( {x - L} \right)}^2}}} + {{K8q} \over {{x^2}}} = 0 \Rightarrow {1 \over {{{\left( {x - L} \right)}^2}}} = {4 \over {{x^2}}}$

or, ${1 \over {x - L}} = {2 \over x} \Rightarrow x = 2x - 2L$

or, $x=2L$
3

AIEEE 2005

A parallel plate capacitor is made by stacking $n$ equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is $'C'$ then the resultant capacitance is
A
$\left( {n + 1} \right)C$
B
$\left( {n - 1} \right)C$
C
$nC$
D
$C$

Explanation

As $n$ plates are joined, it means $(n-1)$ capacitor joined in parallel.

$\therefore$ resultant capacitance $=(n-1)C$
4

AIEEE 2004

A charged oil drop is suspended in a uniform field of $3 \times {10^4}$ $v/m$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $= 9.9 \times {10^{ - 15}}\,\,kg$ and $g = 10\,m/{s^2}$)
A
$1.6 \times {10^{ - 18}}\,C$
B
$3.2 \times {10^{ - 18}}\,C$
C
$3.3 \times {10^{ - 18}}\,C$
D
$4.8 \times {10^{ - 18}}\,C$

Explanation

At equilibrium, electric force on drop balances weight of drop.

$qE = mg \Rightarrow q$

$= {{mg} \over E} = {{9.9 \times {{10}^{ - 15}} \times 10} \over {3 \times {{10}^4}}}$

$= 3.3 \times {10^{ - 18}}C$