### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2005

Two concentric coils each of radius equal to $2$ $\pi$ $cm$ are placed at right angles to each other. $3$ ampere and $4$ ampere are the currents flowing in each coil respectively . The magnetic induction in Weber / ${m^2}$ at the center of the coils will be
$\left( {\mu = 4\pi \times {{10}^{ - 7}}Wb/A.m} \right)$
A
${10^{ - 5}}$
B
$12 \times {10^{ - 5}}$
C
$7 \times {10^{ - 5}}$
D
$5 \times {10^{ - 5}}$

## Explanation

The magnetic field due to circular coil $1$ and $2$ are

${B_1} = {{{\mu _0}{i_1}} \over {2r}} = {{{\mu _0}{i_1}} \over {2\left( {2\pi \times {{10}^{ - 2}}} \right)}}$

$= {{{\mu _0} \times 3 \times {{10}^2}} \over {4\pi }}$

${B_2} = {{{\mu _0}{i_2}} \over {2\left( {2\pi \times {{10}^{ - 2}}} \right)}} = {{{\mu _0} \times 4 \times {{10}^2}} \over {4\pi }}$

$B = \sqrt {B_1^2 + B_2^2} = {{{\mu _0}} \over {4\pi }}.5 \times {10^2}$

$\Rightarrow B = {10^{ - 7}} \times 5 \times {10^2}$

$\Rightarrow B = 5 \times {10^{ - 5}}\,Wb/{m^2}$
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,

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

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

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