 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2007

A charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $\overrightarrow E$ and $\overrightarrow B$ with a velocity $\overrightarrow v$ perpendicular to both $\overrightarrow E$ and $\overrightarrow B,$ and comes out without any change in magnitude or direction of $\overrightarrow v$. Then
A
$\overrightarrow v = \overrightarrow B \times \overrightarrow E /{E^2}$
B
$\overrightarrow v = \overrightarrow E \times \overrightarrow B /{B^2}$
C
$\overrightarrow v = \overrightarrow B \times \overrightarrow E /{B^2}$
D
$\overrightarrow v = \overrightarrow E \times \overrightarrow B /{E^2}$

Explanation

Here, $\overrightarrow E$ and $\overrightarrow B$ are perpendicular to each other and the velocity $\overrightarrow v$ does not change; therefore

$qE = qvB \Rightarrow v = {E \over B}$

Also, $\left| {{{\overrightarrow E \times \overrightarrow B } \over {{B^2}}}} \right| = {{E\,\,B\sin \theta } \over {{B^2}}}$

$= {{E\,\,B\sin {{90}^ \circ }} \over {{B^2}}} = {E \over B} = \left| {\overrightarrow v } \right| = v$
2

AIEEE 2006

A long solenoid has $200$ turns per $cm$ and carries a current $i.$ The magnetic field at its center is $6.28 \times {10^{ - 2}}\,\,\,Weber/{m^2}.$ Another long solenoid has $100$ turns per $cm$ and it carries a current ${i \over 3}$. The value of the magnetic field at its center is
A
$1.05 \times {10^{ - 2}}\,\,Weber/{m^2}$
B
$1.05 \times {10^{ - 5}}\,\,Weber/{m^2}$
C
$1.05 \times {10^{ - 3}}\,\,Weber/{m^2}$
D
$1.05 \times {10^{ - 4}}\,\,Weber/{m^2}$

Explanation

${{{B_2}} \over {{B_1}}} = {{{\mu _0}{n_2}{i_2}} \over {{\mu _0}{n_1}{i_1}}}$

$\Rightarrow {{{B_2}} \over {6.28 \times {{10}^{ - 2}}}} = {{100 \times {i \over 3}} \over {200 \times i}}$

$\Rightarrow {B_2} = {{6.28 \times {{10}^{ - 2}}} \over 6}$

$= 1.05 \times {10^{ - 2}}\,\,Wb/{m^2}$
3

AIEEE 2006

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a
A
helix
B
straight line
C
ellipse
D
circle

Explanation

The charged particle will move along the lines of electric field (and magnetic field). Magnetic field will exert no force. The force by electric field will be along the lines of uniform electric field. Hence the particle will move in a straight line.
4

AIEEE 2006

Needles ${N_1}$, ${N_2}$ and ${N_3}$ are made of ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will
A
attract ${N_1}$ and ${N_2}$ strongly but repel ${N_3}$
B
attract ${N_1}$ strongly, ${N_2}$ weakly and repel ${N_3}$ weakly
C
attract ${N_1}$ strongly, but repel ${N_2}$ and ${N_3}$ weakly
D
attract all three of them

Explanation

Ferromagnetic substance has magnetic domains whereas para-magnetic substances have magnetic dipoles which get attracted to a magnetic field. Diamagnetic substances do not have magnetic dipole but in the presence of external magnetic field due to their orbital motion of electrons these substances are repelled.