I have a hertzian dipole at the origin

[Roodles01]

Homework Statement

I have a hertzian dipole at the origin, generating a signal. Nearby in empty space there is a loop, at a position vector r=(50m)ez_z which can detect this signal.

Homework Equations

I have the equation B(t) = B₀ sin (2*pi*ft)e^x which I understand is the signal emitted by the dipole.

I know that along the z-axis (where the dipole is oriented) there is no magnetic field generated by the electric field & that along the equatorial plane it will be maximum.

It should be specified in spherical coordinates & dipole symmetry means the magnitude of the field is independent of radial angle, Ø. The emitted signal is dependent on angle, θ, though.

The Attempt at a Solution

The loop obviously receives the signal, causing a small current to flow in it, hence it can be measured.

How does the orientation of the loop affect the detection of the signal? Could I explain it in terms of the same equation (above)?
I'm not sure . . . . . . . .
Could someone clarify this please.

 

[mark726]

I would like to clarify the concepts mentioned in the forum post. Firstly, the Hertzian dipole is a theoretical model used to describe the behavior of an antenna that radiates electromagnetic waves. It is often used to represent a simple dipole antenna, which consists of two poles with opposite charges. The dipole is usually oriented along the z-axis, with one pole at the origin and the other pole at a distance of d along the z-axis.

The equation B(t) = B0 sin (2*pi*ft)ex represents the magnetic field generated by the dipole at a distance r from the origin. This equation is correct for points along the z-axis, where the electric field generated by the dipole is zero. However, for points along the equatorial plane (perpendicular to the z-axis), the electric field is maximum and the magnetic field is zero. Therefore, the equation for the magnetic field at these points would be B(t) = 0ex.

Now, for the detection of the signal by the loop located at r=(50m)ezz, the orientation of the loop does affect the detection. The loop will detect the signal only if it is oriented in the same direction as the magnetic field generated by the dipole. In this case, the loop should be oriented along the x-axis (perpendicular to the z-axis). This is because the magnetic field is maximum along this direction, and the loop will experience a maximum induced current.

In terms of the equation mentioned, the orientation of the loop can be taken into account by considering the direction of the unit vector ex. If the loop is oriented along the x-axis, ex will be equal to (1,0,0) and the equation for the magnetic field will be B(t) = B0 sin (2*pi*ft)(1,0,0). If the loop is oriented along any other direction, the equation will have to be modified accordingly.

I hope this explanation helps in understanding the role of orientation in the detection of the signal by the loop.