Introduction:
The half power beam width (HPBW) is a measure of the angular width of the radiation pattern of an antenna. It is defined as the angle between the two points on the radiation pattern where the power is half of the maximum power. In the case of a Hertz dipole antenna, the HPBW in the E-plane is 90 degrees.

Explanation:
To understand why the HPBW in the E-plane for a Hertz dipole antenna is 90 degrees, we need to consider the antenna's radiation pattern and the properties of the E-plane.

Hertz Dipole Antenna:
A Hertz dipole antenna is a simple antenna consisting of a straight conductor with a length equal to a half-wavelength. It is typically used for radiation or reception of electromagnetic waves in the radio frequency range.

Radiation Pattern:
The radiation pattern of an antenna depicts the distribution of radiated power as a function of direction. In the case of a Hertz dipole antenna, the radiation pattern is omnidirectional in the azimuthal plane (horizontal plane) and has a toroidal shape in the elevation plane (vertical plane).

E-plane:
The E-plane is a plane that contains the direction of maximum radiation from the antenna and is perpendicular to the azimuthal plane. In other words, it is the plane in which the electric field vector is perpendicular to the direction of propagation.

Half Power Beam Width:
The HPBW is the angular width of the main lobe of the radiation pattern, where the power is half of the maximum power. For a Hertz dipole antenna, the radiation pattern in the E-plane is toroidal, and the maximum radiation occurs in the perpendicular direction to the E-plane (azimuthal plane). Therefore, the HPBW in the E-plane is 90 degrees.

Conclusion:
In summary, the HPBW in the E-plane for a Hertz dipole antenna is 90 degrees because the radiation pattern in the E-plane is toroidal, and the maximum radiation occurs in the perpendicular direction to the E-plane. This means that the power is half of the maximum power at an angular distance of 90 degrees from the direction of maximum radiation.

The beam-width of Hertzian dipole is 180° and its half power beam-width is 90°.