An antenna is connected to a car battery. Will the antenna emit electromagnetic radiation? Why or why not? Explain

Only during hookup and disconnect when the current is changing. To get a radiating wave you need changing current (in the simplest case, an accelerating charge radiates; look that up in your text or Google it. Normally you radiate using a sinusoidal signal of a frequency with a wavelength matched to the antenna. However using Fourier transforms, any old changing signal can be made up of sine waves. However just a steady direct current just gives stationary electric and magnetic fields, no Poynting vector, no radiated signal.

This might help:

http://www.youtube.com/watch?v=IWVPJSoJDzA
and this:
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/emwv.html

Good question by the way :)

Yes, the antenna will emit electromagnetic radiation when connected to a car battery. To understand why, let's explore the principles of how an antenna works.

An antenna is a conductor that is designed to radiate or receive electromagnetic waves, typically in the form of radio waves or microwaves. When an electric current passes through the antenna, it generates an alternating magnetic field around it. This alternating magnetic field, in turn, creates an alternating electric field, which propagates as an electromagnetic wave.

In this scenario, when the antenna is connected to a car battery, an electric current flows through it. The battery acts as a power source, providing a potential difference, which causes the current to flow from the positive terminal to the negative terminal of the battery. As the current passes through the antenna, it creates the alternating magnetic field mentioned earlier.

The electromagnetic wave generated by the antenna usually falls within the radio frequency range. These radio waves can propagate through free space or other medium and carry energy with them. The intensity and frequency of the electromagnetic radiation emitted by the antenna depend on various factors such as the shape, size, and design of the antenna.

Therefore, when an antenna is connected to a car battery, it will emit electromagnetic radiation in the form of radio waves or microwaves, provided that the antenna is designed and operated for that purpose.