An electromagnetic wave in terms of oscillation of magnetic field is given as B → = B 0 sin ω t - k y k ^ . T. The corresponding electric field oscillation is given by

E → = B 0 c sin ω t - k y - i ^ N C

E → = B 0 c sin ω t - k y j ^ N C

E → = B 0 c sin ω t - k y i ^ N C

E → = B 0 c sin ω t - k x k ^ N C

If dimensions of ε 0 d ϕ E d t is M a L b T c A d , then value of ( a + b + c + d ) is _____ .

We know that ϕ = E → · A → The dimensional formula of area is M 0 L 2 T 0 . Since E l e c t r i c f i e l d = F o r c e c h a r g e Dimensional formula for electric field will be M 1 L 1 T - 2 × I 1 T 1 - 1 = M 1 L 1 T - 3 I - 1 So the dimensional formula for flux will be M 1 L 1 T - 3 I - 1 × M 0 L 2 T 0 = M 1 L 3 T - 3 I - 1 The dimensional formula for ε 0 will be M - 1 L - 3 T 4 I 2 . So the dimensional formula for ε 0 d ϕ E d t will be M 1 L 3 T - 3 I - 1 × M - 1 L - 3 T 4 I 2 × T - 1 = M 0 L 0 T 0 I 1 Given that M 0 L 0 T 0 I 1 = M a L b T c I d So a + b + c + d = 1

For an electromagnetic wave described by B = 8 × 10 - 6 sin 5000 π x - 3 × 10 11 π t , where B is in tesla, x is in metre and t is in second. If speed of wave is N × 10 7 m s - 1 , then value of N is _____ .

Given that an electromagnetic wave propagating through vacuum is given by B = 8 × 10 - 6 sin 5000 πx - 3 × 10 11 πt where x is in metre and t is in second. From the equation we can see that ω = 3 . 0 × 10 11 π and k = 5000 π . We know that c = ω k . ⇒ c = ω k = 3 . 0 × 10 11 π 5000 π ⇒ c = 6 × 10 7 m s - 1 . Given that the speed of wave is N × 10 7 m s - 1 . So the value of N is 6 .

The electric field of a plane electromagnetic wave is given by E = E 0 sin ( k z - ω t ) [ i ^ + j ^ ] . If direction of the associated magnetic field is a i ^ + b j ^ , then value of ( a + b ) is _____ .

Given that the electric field of a plane electromagnetic wave is given by E = E 0 sin ( k z - ω t ) [ i ^ + j ^ ] Given that the direction of the associated magnetic field is a i ^ + b j ^ . We know that the electric and magnetic fields propagate in perpendicular directions to each other. So we can say that, E → · B → = 0 ⇒ E 0 sin ( k z - ω t ) [ i ^ + j ^ ] · a i ^ + b j ^ = 0 ⇒ E 0 sin ( k z - ω t ) × a + E 0 sin ( k z - ω t ) × b = 0 ⇒ E 0 sin ( k z - ω t ) a + b = 0 ⇒ a + b = 0 So the value of a + b = 0 .

E M B I B E

Gamma Question Bank for Engineering Physics>Chapter 22 - Electromagnetic Waves>Assignment Set-2>Q 30

MEDIUM

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IMPORTANT

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The average value of electric energy density in an electromagnetic wave is $($ $E_{0}$ is peak value $)$ )

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Important Questions on Electromagnetic Waves

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 22 - Electromagnetic Waves>Assignment Set-2>Q 31

The electric displacement current through a surface area

S

is proportional to the

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 22 - Electromagnetic Waves>Assignment Set-2>Q 32

An EM wave defined by

E = E_{0} \sin (k x - ω t)

is passing through free space, the quantity which is independent of the wavelength, is

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IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 22 - Electromagnetic Waves>Assignment Set-2>Q 33

The energy stored in a

1.2 m

length of a laser beam operating at

5 mW

will be

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IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 22 - Electromagnetic Waves>Assignment Set-2>Q 34

The oscillating magnetic field in a plane electromagnetic wave is given as $B_{z} = 8 \times 10^{- 6} \sin (1000 π x - 3 \times 10^{11} π t)$ where $B_{z}$ is in tesla, $x$ is in metre and $t$ is in second. The amplitude of the oscillating electric field will be