1

### JEE Main 2019 (Online) 10th January Evening Slot

The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression $\overrightarrow E \left( {x,y} \right) = 10\widehat j\cos \left[ {\left( {6x + 8z} \right)} \right].$ The magnetic field $\overrightarrow B$(x,z, t) is given by $-$ (c is the velocity of light)
A
${1 \over c}\left( {6\hat k + 8\widehat i} \right)\cos \left[ {\left( {6x + 8z - 10ct} \right)} \right]$
B
${1 \over c}\left( {6\widehat k - 8\widehat i} \right)\cos \left[ {\left( {6x + 8z - 10ct} \right)} \right]$
C
${1 \over c}\left( {6\hat k + 8\widehat i} \right)\cos \left[ {\left( {6x - 8z + 10ct} \right)} \right]$
D
${1 \over c}\left( {6\hat k - 8\widehat i} \right)\cos \left[ {\left( {6x - 8z + 10ct} \right)} \right]$

## Explanation

$\overrightarrow E = 10\widehat j\cos \left[ {\left( {6\widehat i + 8\widehat k} \right).\left( {x\widehat i + z\widehat k} \right)} \right]$

$= 10\widehat j\,\cos \left[ {\overrightarrow K .\overrightarrow r } \right]$

$\therefore$   $\overrightarrow K = 6\widehat i + 8\widehat k;$ direction of waves travel.

i.e., direction of 'c'. $\therefore$   Direction of $\widehat B$ will be along

$\widehat C \times \widehat E = {{ - 4\widehat i + 3\widehat k} \over 5}$

Mag. of $\overrightarrow B$ will be along

$\widehat C \times \widehat E = {{ - 4\widehat i + 3\widehat k} \over 5}$

Mag. of $\overrightarrow B = {E \over C} = {{10} \over C}$

$\therefore$   $\overrightarrow B = {{10} \over C}\left( {{{ - 4\widehat i + 3\widehat k} \over 5}} \right) = {{\left( { - 8\widehat i + 6\widehat k} \right)} \over C}$
2

### JEE Main 2019 (Online) 11th January Morning Slot

An electromagnetic wave of intensity 50 Wm–2 enters in a medium of refractive index 'n' without any loss. The ratio of the magnitudes of electric, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by:
A
$\left( {{1 \over {\sqrt n }},{1 \over {\sqrt n }}} \right)$
B
$\left( {\sqrt n ,\sqrt n } \right)$
C
$\left( {\sqrt n ,{1 \over {\sqrt n }}} \right)$
D
$\left( {{1 \over {\sqrt n }},\sqrt n } \right)$

## Explanation

C $= {1 \over {\sqrt {{\mu _0}{ \in _0}} }}$

V = $= {1 \over {\sqrt {k{ \in _0}{\mu _0}} }}$ [For transparent medium $\mu$r $\approx$ $\mu$0]

$\therefore$  ${C \over V}$ $=$ $\sqrt k =$ n

${1 \over 2} \in {}_0\,E_0^2$C $=$ intensity $=$ ${1 \over 2}$$\in$0 kE2v

$\therefore$   E$_0^2$C $=$ kE2v

$\Rightarrow$  ${{E_0^2} \over {{E^2}}} = {{kV} \over C} = {{{n^2}} \over n} \Rightarrow {{{E_0}} \over E} = \sqrt n$

similarly

${{B_0^2C} \over {2{\mu _0}}} = {{{B^2}v} \over {2{\mu _0}}} \Rightarrow {{{B_0}} \over B} = {1 \over {\sqrt n }}$
3

### JEE Main 2019 (Online) 11th January Evening Slot

A 27 mW laser beam has a cross-sectional area of 10 mm2. The magnitude of the maximum electric field in this electromagnetic wave is given by :
[Given permittivity of space $\in$0 = 9 $\times$ 10–12 SI units, Speed of light c = 3 $\times$ 108 m/s]
A
2 kV/m
B
1 kV/m
C
1.4 kV/m
D
0.7 kV/m

## Explanation

Intensity of EM wave is given by

${\rm I} = {{Power} \over {Area}} = {1 \over 2}{\varepsilon _0}E_0^2C$

$= {{27 \times {{10}^{ - 3}}} \over {10 \times {{10}^{ - 6}}}}$ $= {1 \over 2} \times 9 \times {10^{ - 12}} \times {E^2} \times 3 \times {10^8}$

$E = \sqrt 2 \times {10^3}kv/m$

$= 1.4$ kv/m
4

### JEE Main 2019 (Online) 11th January Evening Slot

A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 $\times$ 10–6 J/ T when a magnetic intensity of 60 $\times$ 103 A/m is applied. Its magnetic susceptibility is
A
3.3 $\times$ 10–4
B
2.3 $\times$ 10–2
C
4.3 $\times$ 10–2
D
3.3 $\times$ 10–2

## Explanation

x = ${1 \over H}$

I = ${{Magnetic\,moment} \over {Volume}}$

I = ${{20 \times {{10}^{ - 6}}} \over {{{10}^{ - 6}}}}$ = 20 N/m2

x = ${{20} \over {60 \times {{10}^{ + 3}}}}$ = ${1 \over 3} \times {10^{ - 3}}$

= 0.33 $\times$ 10$-$3 = 3.3 $\times$ 10$-$4