 JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2004

The magnetic field due to a current carrying circular loop of radius $3$ $cm$ at a point on the axis at a distance of $4$ $cm$ from the centre is $54\,\mu T.$ What will be its value at the center of loop?
A
$125\,\mu T$
B
$150\,\mu T$
C
$250\,\mu T$
D
$75\,\mu T$

Explanation

The magnetic field at a point on the axis of a circular loop at a distance $x$ from center is,

$B = {{{\mu _0}i\,{a^2}} \over {2\left( {{x^2} + {a^2}} \right)3/2}}$ $\,\,\,\,\,B' = {{{\mu _0}i} \over {2a}}$

$\therefore$ $B' = {{B.{{\left( {{x^2} + {a^2}} \right)}^{3/2}}} \over {{a^3}}}$

Put $x = 4$ & $a = 3 \Rightarrow B' = {{54\left( {{5^3}} \right)} \over {3 \times 3 \times 3}} = 250\mu T$
2

AIEEE 2004

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $B.$ It is then bent into a circular loop of $n$ turns. The magnetic field at the center of the coil will be
A
$2n$ $B$
B
${n^2}\,B$
C
$nB$
D
$2{n^2}\,B$

Explanation

KEY CONCEPT : Magnetic field at the center of a circular coil of radius $R$ carrying

current is $B = {{{\mu _0}i} \over {2R}}$

Given: $n \times \left( {2\pi r'} \right) = 2\pi R$

$\Rightarrow nr' = R\,\,\,\,\,\,\,\,\,\,\,...\left( 1 \right)$

$B' = {{n.{\mu _0}i} \over {2r'}}\,\,\,\,\,\,\,\,\,\,\,...\left( 2 \right)$

from $\left( 1 \right)$ and $\left( 2 \right),$ $B' = {{n{\mu _0}i.n} \over {2\pi R}} = {n^2}B$
3

AIEEE 2004

A current $i$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is
A
${{{\mu _0}} \over {4\pi }},{{2i} \over r}$ tesla
B
zero
C
infinite
D
${{2i} \over r}$ tesla

Explanation

Using Ampere's law at a distance $r$ from axis, $B$ is same from symmetry.

$\int {B.dl = {\mu _0}i}$

i.e., $B \times 2\pi r = {\mu _0}i$

Here $i$ is zero, for $r < R,$ whereas $R$ is the radius

$\therefore$ $B=0$
4

AIEEE 2004

Curie temperature is the temperature above which
A
a ferromagnetic material becomes paramagnetic
B
a paramagnetic material becomes diamagnetic
C
a ferromagnetic material becomes diamagnetic
D
a paramagnetic material becomes ferromagnetic

Explanation

KEY CONCEPT : The temperature above which a ferromagnetic substance becomes para-magnetic is called Curie's temperature.