An electromagnetic wave travels in vacuum with electric field as:

$\overset{?}{E} = E_{1} \hat{i} c o s ? (k z - ω t) + E_{2} \hat{j} c o s ? (k z + ω t)$ .

The associated magnetic field is given as:

Option 1 -

$\vec{B} = \frac{1}{c} (E_{1} \hat{i} - E_{2} \hat{j}) c o s (k z - ω t)$

Option 2 -

$\vec{B} = \frac{1}{c} (E_{1} \hat{i} + E_{2} \hat{j}) c o s (k z + ω t)$

Option 3 -

$\vec{B} = \frac{E_{1}}{c} \hat{j} c o s (k z - ω t) + \frac{E_{2}}{c} \hat{i} c o s (k z + ω t)$

Option 4 -

$\vec{B} = \frac{E_{1}}{c} \hat{i} c o s (k z - ω t) + \frac{E_{2}}{c} \hat{j} c o s (k z + ω t)$

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1 Answer

Answered by

Raj Pandey | Contributor-Level 9

2 months ago

Correct Option - 3

Detailed Solution:

${\overset{?}{B}}_{1} = \frac{E_{1}}{c} c o s ? (k z - ω t) {\overset{?}{B}}_{1}$ where ${\overset{?}{B}}_{1} = {\hat{c}}_{1} \times {\overset{?}{E}}_{1} = \hat{k} \times \hat{i} = {\overset{?}{B}}_{1} = \hat{j}$

${\overset{?}{B}}_{2} = \frac{E_{2}}{c} c o s ? (k z + ω t) {\overset{?}{B}}_{2}$ where ${\overset{?}{B}}_{2} = {\hat{c}}_{2} \times {\overset{?}{E}}_{2} = - \hat{k} \times \hat{j} = {\overset{?}{B}}_{2} = \hat{i}$

$∴ \overset{?}{B} = {\overset{?}{B}}_{1} + {\overset{?}{B}}_{2}$

$\overset{?}{B} = \frac{E_{1}}{c} \hat{j} c o s ? (k z - ω t) + \frac{E_{2}}{c} \hat{i} c o s ? (k z + ω t)$

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An electromagnetic wave travels in vacuum with electric field as:

$\overset{?}{E} = E_{1} \hat{i} c o s ? (k z - ω t) + E_{2} \hat{j} c o s ? (k z + ω t)$ .

The associated magnetic field is given as:

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An electromagnetic wave travels in vacuum with electric field as: E ? = E 1 i ˆ c o s ? ( k z - ω t ) + E 2 j ˆ c o s ? ( k z + ω t ) . The associated magnetic field is given as:

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An electromagnetic wave travels in vacuum with electric field as:

$\overset{?}{E} = E_{1} \hat{i} c o s ? (k z - ω t) + E_{2} \hat{j} c o s ? (k z + ω t)$ .

The associated magnetic field is given as: