Problem 10 - University Physics with Modern Physics

Question

A dipole antenna is located at the origin with its axis along the \(z\) -axis. As electric current oscillates up and down the antenna, polarized electromagnetic radiation travels away from the antenna along the positive \(y\) -axis. What are the possible directions of electric and magnetic fields at point \(A\) on the \(y\) -axis? Explain.

Step-by-Step Solution

Answer

Answer: At point A on the y-axis, the possible directions of the electric field are parallel to the z-axis, and the possible directions of the magnetic field are parallel to the x-axis.

Step 1: Understand dipole antenna radiation mechanism

The dipole antenna has its axis along the z-axis, and current oscillates up and down along this axis, producing electromagnetic radiation. The radiation is polarized, and it is emitted along the positive y-axis.

Step 2: Identify coordinates and directions

We need to find the direction of the electric and magnetic fields at point A, which is on the y-axis. The y-axis is the direction of propagation, meaning that the radiation is emitted along this axis. Since the electric field is always perpendicular to the magnetic field, and the fields must also be perpendicular to the direction of propagation (y-axis), these fields must lie on the xz-plane.

Step 3: Determine electric field direction

At point A on the y-axis, since the electric field must be perpendicular to the y-axis, the possible directions of the electric field should be in the xz-plane. Because the antenna's axis is along the z-axis and electric current oscillates along this axis, EM radiation is polarized in the z-axis, making the electric field parallel to the z-axis at point A. The electric field direction at point A is parallel to the z-axis.

Step 4: Determine magnetic field direction

To find the direction of the magnetic field at point A, we can use the property that the magnetic field is always perpendicular to the electric field and the direction of propagation. Since the electric field lies along the z-axis, and the direction of propagation is along the y-axis, the magnetic field must be along the x-axis. The magnetic field direction at point A is parallel to the x-axis. In conclusion, at point A on the y-axis, the possible directions of the electric field are parallel to the z-axis, and the possible directions of the magnetic field are parallel to the x-axis.