An electromagnetic wave is propagating in vacuum along -{j} direction. The magnetic field of the wave is given by {B} = (2 × 10^{-8}) ≤ft[π × 10¹5} ≤ft(t + y/c)] {k} { T}. The electric field {E} of this wave is (c speed of light)

Correct Answer is : E⃗=(6)cos⁡[π×1015(t+yc)]i^ V/m{E} = (6) [π × 10¹5} ≤ft(t + y/c)] {i} \;\; {V} / {m}E=(6)cos[π×1015(t+cy)]i^V/m

{E} = (4) [π × 10¹5} ≤ft(t + y/c)] {j} \;\; {V} / {m}

{E} = (6) [π × 10¹5} ≤ft(t + y/c)] {i} \;\; {V} / {m}

{E} = (6) [π × 10¹5} ≤ft(t - y/c)] {j} \;\; {V} / {m}

{E} = (4) [π × 10¹5} ≤ft(t - y/c)] {i} \;\; {V} / {m}

Correct Answer is : E⃗=(6)cos⁡[π×1015(t+yc)]i^ V/m{E} = (6) [π × 10¹5} ≤ft(t + y/c)] {i} \;\; {V} / {m}E=(6)cos[π×1015(t+cy)]i^V/m

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TS EAMCET 18-July-2022 Shift 1 Solved Paper

Section: Physics

Question : 113 of 160

Marks: +1, -0

-\hat{j}

\vec{B} = (2 \times 10^{-8}) \cos\left[\pi \times 10^{15} \left(t + \frac{y}{c}\right)\right] \hat{k} \text{ T}

\vec{E}

(c \equiv

speed of light)

$\vec{E} = (4) \cos[\pi \times 10^{15} \left(t + \frac{y}{c}\right)] \hat{j} \;\; \text{V} / \text{m}$
$\vec{E} = (6) \cos[\pi \times 10^{15} \left(t + \frac{y}{c}\right)] \hat{i} \;\; \text{V} / \text{m}$
$\vec{E} = (6) \cos[\pi \times 10^{15} \left(t - \frac{y}{c}\right)] \hat{j} \;\; \text{V} / \text{m}$
$\vec{E} = (4) \cos[\pi \times 10^{15} \left(t - \frac{y}{c}\right)] \hat{i} \;\; \text{V} / \text{m}$

Solution:

Expression for the magnetic field of EM wave is given as

B = (2 \times 10^{-8}) \cos[\pi \times 10^{15} \left(t + \frac{y}{c}\right)] \hat{k} \text{ T}

Magnitude of magnetic field vector,

B_0 = 2 \times 10^{-8} \text{ T}

Magnitude of electric field vector of EM wave,

E_0 = B_0 c

where,

c

is speed of light

= 2 \times 10^{-8} \times 3 \times 10^{8}

= 6 \text{ V} / \text{m} \;\; (\because c = 3 \times 10^{8} \text{ m} / \text{s})

\hat{n}

be the unit vector along the direction of electric field, then we know that unit vector along electric field vector

x

Unit vector along magnetic field vector

=

Unit vector along the direction of propagation of EM wave.

i.e.

\hat{n} \times \hat{k} = -\hat{j}

clearly,

\hat{n} = \hat{i}

Hence, expression of electric field vector of EM wave,

E = 6 \cos[\pi \times 10^{15} \left(t + \frac{y}{c}\right)] \hat{i} \text{ V} / \text{m}

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