### JEE Mains Previous Years Questions with Solutions

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1

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

### 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

$\therefore$ $B=0$
3

### 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.
4

### AIEEE 2003

The magnetic lines of force inside a bar magnet
A
are from north-pole to south-pole of the magnet
B
do not exist
C
depend upon the area of cross-section of the bar magnet
D
are from south-pole to north-pole of the Magnet

## Explanation

As shown in the figure, the magnetic lines of force are directed from south to north inside a bar magnet.