For Poynting vector, following are given : (A) Poynting Vector around a point source is radial.

 

57) For Poynting vector, following are given :

• (A) Poynting Vector around a point source is radial.
• (B) There are only E_θ & H_φ present and are transverse.
• (C) There is only E_φ component is present
• (D) There is only E_θ is present
• (E) Poynting vector does not exist around a point source

Choose the correct answer from the options given below :

• (1) (A) and (B) only
• (2) (B) and (E) only
• (3) (B) and (D) only
• (4) (A) and (E) only

Answer: A

Analysis of the Statements:

• Definition: The Poynting Vector represents the directional energy flux of an electromagnetic field and is given by the cross product: 

  $\mathbf{S}=\mathbf{E}\times \mathbf{H}$

  .

• (A) Poynting Vector around a point source is radial:
  Correct. A point source radiates energy outward in all directions. In spherical coordinates 

  $(r,\theta ,\varphi )$

  , the energy flows away from the center along the radius. Therefore, the Poynting vector has only a radial component (

  $S_r$

  ).

• (B) There are only 

  $E_{\theta }$

   and 

  $H_{\varphi }$

   present and are transverse:
  Correct. In the far-field (radiation zone) of a typical point source model like a Hertzian dipole, the electromagnetic waves become transverse. The electric field (

  $\mathbf{E}$

  ) typically has a polar component (

  $E_{\theta }$

  ) and the magnetic field (

  $\mathbf{H}$

  ) has an azimuthal component (

  $H_{\varphi }$

  ). Since 

  $\mathbf{S}=\mathbf{E}\times \mathbf{H}=(E_{\theta }\widehat{\theta })\times (H_{\varphi }\widehat{\varphi })=(E_{\theta }{H}_{\varphi })\widehat{r}$

  , this confirms that the fields are transverse to the direction of propagation (radial) and to each other.

• (C) & (D) Only one field component is present:
  Incorrect. You need both an electric field (

  $\mathbf{E}$

  ) and a magnetic field (

  $\mathbf{H}$

  ) to have a non-zero Poynting vector. One alone does not result in energy propagation.

• (E) Poynting vector does not exist around a point source:
  Incorrect. Any source that radiates electromagnetic energy has an associated Poynting vector.

Conclusion:

Statements (A) and (B) are correct.

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