276. The spectral density of pink noise varies as—

1. 1. 1/f²

   
   
   

   2. f²

   
   
   

   3. 1/f

   
   
   

   4. f

   
   
   

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1. View Hint View Answer Discuss in Forum

   The spectral density of pink noise varies as 1/f².
   

   Correct Option: A

   The spectral density of pink noise varies as 1/f².
   

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277. When an iron core is placed between the poles of a permanent magnet as shown in figure below, the magnetic field pattern is—

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. 

   
   
   

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1. View Hint View Answer Discuss in Forum

   Figure (C) is the best answer.

   Correct Option: C

   Figure (C) is the best answer.

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278. For an infinite linear current, four loops are shown in the given figure. The magnetic flux should be the maximum through the loop number—
     

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   All the loops have equal areas. B at any distance r from the wire is k/ r. For any rectangular loop of height h (in the direction of the wire) and width w (⊥ the wire), the flux φ is
   

   	a + w	khdr	∞	= kh ln	a + w
   	a	r			a

   
   where a is the distance of the near side from the wire.
   Thus,
   

   for 1, φ1 = k l ln	a + 1
   	a

   
   

   for 2, φ2 = k 2l ln	a + 1/2
   	a

   
   

   for 3, φ3 =	1	k2l ln	a + 1/4 + 1
   	2		a + 1/4

   
   

   for 4, φ4 =	kl ln	a + 2 l
   		a

   
   

   φ1 = kl ln		1 +	1		,φ2 = 2kl ln		1 +	1
   			a					a

   
   

   φ3 = kl ln

   1 +

   1

   ,φ4 =

   1

   kl ln

   1 +

   2 l

   a + 1/4

   2

   a

   
   The long terms do not change by significant amount. Thus, φ₂ should be of highest value.
   Hence alternative (B) is the correct choice.
   

   Correct Option: B

   All the loops have equal areas. B at any distance r from the wire is k/ r. For any rectangular loop of height h (in the direction of the wire) and width w (⊥ the wire), the flux φ is
   

   	a + w	khdr	∞	= kh ln	a + w
   	a	r			a

   
   where a is the distance of the near side from the wire.
   Thus,
   

   for 1, φ1 = k l ln	a + 1
   	a

   
   

   for 2, φ2 = k 2l ln	a + 1/2
   	a

   
   

   for 3, φ3 =	1	k2l ln	a + 1/4 + 1
   	2		a + 1/4

   
   

   for 4, φ4 =	kl ln	a + 2 l
   		a

   
   

   φ1 = kl ln		1 +	1		,φ2 = 2kl ln		1 +	1
   			a					a

   
   

   φ3 = kl ln

   1 +

   1

   ,φ4 =

   1

   kl ln

   1 +

   2 l

   a + 1/4

   2

   a

   
   The long terms do not change by significant amount. Thus, φ₂ should be of highest value.
   Hence alternative (B) is the correct choice.
   

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279. Consider the following statements regarding Maxwell's equations in differential form (symbols have their usual meaning)
     1. For free space ∇ × H = (σ + jω ε) E
     2. For free space ∇. D = ρ
     3. For steady current ∇ × H = j
     4. For static electric field ∇. D = ρ
     of these statements—

1. 1. 1 and 2 are correct

   
   
   

   2. 2 and 3 are correct

   
   
   

   3. 3 and 4 are correct

   
   
   

   4. 1 and 4 are correct

   
   
   

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1. View Hint View Answer Discuss in Forum

   For free space σ and ρ are each zero. Thus, statements 3 and 4 are correct.

   Correct Option: C

   For free space σ and ρ are each zero. Thus, statements 3 and 4 are correct.

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280. A plane wave propagating through a medium [E_r = 8, V_r = 2 and σ = 0] has its electric field given by
     

     →	^
     E = 0.5	ax	e–(z/3) sin (108 t – β2) V/m

     . The wave impedance in ohms is—

1. 1. 377

   
   
   

   2. 198.5 ∠180º

   
   
   

   3. 182.9 ∠14º

   
   
   

   4. 133.3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Wave impedance of medium is given by
   

   | n | =	Exs	=	0.50^α xe–(z/3) sin (108 t – β2)
   	Hys		Hy5

   
   

   =	0.5	n0 = 377 Ω
   	√μr/εr

   Correct Option: A

   Wave impedance of medium is given by
   

   | n | =	Exs	=	0.50^α xe–(z/3) sin (108 t – β2)
   	Hys		Hy5

   
   

   =	0.5	n0 = 377 Ω
   	√μr/εr

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