Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by E = $20 c o s (2 \times 1 0^{10} t - 200 x) V / m .$ The dielectric constant of the medium is equal to:

(Take $μ_{r} = 1)$

Option 1 -

$\frac{1}{3}$

Option 2 -

Option 3 -

Option 4 -

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 4

Detailed Solution:

Comparing E = 20 cos (2 × 10¹⁰ t – 200x) V/m to

$E = E_{0} c o s (ω t - k x) v / m$

$ω = 2 \times 1 0^{10}, K = 200$

Speed = $\frac{2 \times 1 0^{10}}{200} = 1 0^{8} m / s$

R.I. $= \frac{C}{s p e e d} = \frac{3 \times 1 0^{8}}{1 0^{8}} = 3$

$N o w R . I . = \sqrt[]{ε_{r} μ_{r}}$

$3 = \sqrt[]{ε_{r} \times 1}$

$ε_{r} = 9$

Comparing E = 20 cos (2 × 1010 t – 200x) V/m to <math> <mrow> <mi>E</mi> <mo>=</mo> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mrow> <mi>ω</mi> <mi>t</mi> <mo>−</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mi>v</mi> <mo>/</mo> <mi>m</mi> </mrow> </math>               <math> <mrow> <mi>ω</mi> <mo>=</mo> <mn>2</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> </mrow> </msup> <mo>,</mo> <mi>K</mi> <mo>=</mo> <mn>2</mn> <mn>0</mn> <mn>0</mn> </mrow> </math>               Speed = <math> <mrow> <mfrac> <mrow> <mn>2</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <mn>0</mn> <mn>0</mn> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>8</mn> </mrow> </msup> <mi>m</mi> <mo>/</mo> <mi>s</mi> </mrow> </math>  R.I. <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> </mrow> <mrow> <mi>s</mi> <mi>p</mi> <mi>e</mi> <mi>e</mi> <mi>d</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>8</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>8</mn> </mrow> </msup> </mrow> </mfrac> <mo>=</mo> <mn>3</mn> </mrow> </math>   <math> <mrow> <mi>N</mi> <mi>o</mi> <mi>w</mi> <mtext> </mtext> <mtext> </mtext> <mi>R</mi> <mo>.</mo> <mi>I</mi> <mo>.</mo> <mo>=</mo> <mroot> <mrow> <msub> <mrow> <mi>ε</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <mn>3</mn> <mo>=</mo> <mroot> <mrow> <msub> <mrow> <mi>ε</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <mo>×</mo> <mn>1</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>ε</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>9</mn> </mrow> </math>

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Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by E = $20 c o s (2 \times 1 0^{10} t - 200 x) V / m .$ The dielectric constant of the medium is equal to:

(Take $μ_{r} = 1)$

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Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by E = 2 0 c o s ( 2 × 1 0 1 0 t − 2 0 0 x ) V / m . The dielectric constant of the medium is equal to: (Take μ r = 1 )

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Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by E = $20 c o s (2 \times 1 0^{10} t - 200 x) V / m .$ The dielectric constant of the medium is equal to:

(Take $μ_{r} = 1)$