 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2005

A charged particle of mass $m$ and charge $q$ travels on a circular path of radius $r$ that is perpendicular to a magnetic field $B.$ The time taken by the particle to complete one revolution is
A
${{2\pi {q^2}B} \over m}$
B
${{2\pi mq} \over B}$
C
${{2\pi m} \over {qB}}$
D
${{2\pi qB} \over m}$

Explanation

Equating magnetic force to centripetal force.

${{m{V^2}} \over r} = qvB\,\sin \,{90^ \circ }$

Time to complete one revolution.

$T = {{2\pi r} \over v} = {{2\pi m} \over {qB}}$
2

AIEEE 2005

Two thin, long, parallel wires, separated by a distance $'d'$ carry a current of $'i'$ $A$ in the same direction. They will
A
repel each other with a force of ${\mu _0}{i^2}/\left( {2\pi d} \right)$
B
attract each other with a force of ${\mu _0}{i^2}/\left( {2\pi d} \right)$
C
repel each other with a force $_0{i^2}/\left( {2\pi {d^2}} \right)$
D
attract each other with a force of ${\mu _0}{i^2}/\left( {2\pi {d^2}} \right)$

Explanation

${F \over \ell } = {{{\mu _0}{i_1}} \over {2\pi d}} = {{{\mu _0}{i^2}} \over {2\pi d}}$ (attractive as current is in the same direction)
3

AIEEE 2004

The materials suitable for making electromagnets should have
A
high retentivity and low coercivity
B
low retentivity and low coercivity
C
high retentivity and high coercivity
D
low retentivity and high coercivity

Explanation

NOTE : Electro magnet should be amenable to magnetization & demagnetization.

$\therefore$ retentivity should be low & coercivity should be low
4

AIEEE 2004

Two long conductors, separated by a distance $d$ carry current ${I_1}$ and ${I_2}$ in the same direction. They exert a force $F$ on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is
A
$- {{2F} \over 3}$
B
${F \over 3}$
C
$-2F$
D
$- {F \over 3}$

Explanation

Force between two long conductor carrying current,

$F = {{{\mu _0}} \over {4\pi }}{{2{I_1}{I_2}} \over d} \times \ell$

$F' = - {{{\mu _0}} \over {4\pi }}{{2\left( {2{I_1}} \right){I_2}} \over {3d}}\ell$

$\therefore$ ${{F'} \over F} = {{ - 2} \over 3}$