Why doesn't Venus have a magnetic field? How does the speed of rotation affect the magnetic field of a planet? Why doesn't Venus have a magnetic field? How does the speed of rotation affect the magnetic field of a planet?
 A: You hit on the answer in your question. Earth's magnetic field is due to circulating currents of molten metal in the core, movement of which is assisted by the Earth's rapid rotation. Venus's slow rotation is the reason behind its negligible magnetic field. However, it does have a very slight magnetic field which is generated by the interaction of the solar wind and currents in the upper atmosphere. It has been suggested that Earth's magnetic field briefly disappears during magnetic reversals, which happen roughly once every 260,000 years, but that has yet to be proved. 
A: The Earth does have a magnetic field. It is generated by the current of the flowing molten iron outer core.


Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from the Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic field is generated by electric currents due to the motion of convection currents of molten iron in the Earth's outer core: these convection currents are caused by heat escaping from the core, a natural process called a geodynamo.


https://en.wikipedia.org/wiki/Earth%27s_magnetic_field
Now it is a misconception that Venus does not have a magnetic field. 


The interesting thing, however, is that spacecraft observations, like the ones made by ESA's Venus Express, have shown that the ionosphere of Venus direct interaction with the solar winds causes an externally induced magnetic field, which deflects the particles from the solar winds and protects the atmosphere from being blown away from the planet.
    However, the article also explains that the Venus magnetosphere is not as protective as earth's magnetosphere. Measurements of the Venus magnetic field show several similarities, such as deflection of the solar winds and the reconnections in the tail of the magnetosphere, causing plasma circulations in the magnetosphere. The differences might explain the fact that some gasses and water are lost from the Venus atmosphere. The magnetic field of Venus is about 10 times smaller as the earth's magnetic field. The shape of the magnetic field is also different. Earth has a more sharp magnetotail facing away from the sun and Venus has a more comet shaped magnetotail. During the reconnections most of the plasma is lost in the atmosphere.


https://astronomy.stackexchange.com/questions/10189/why-did-venus-not-lose-its-atmosphere-without-magnetic-field
So basically the difference is the source of the magnetic field. 
On Earth, it is a flowing current. On Venus, it is the Ionosphere itself.
A: Some good answers already.  I want to add that it's not exactly known why Venus doesn't have a core generated magnetic field, though it's slow rotation may play a role in that.
Mercury has a slow rotation and Mercury has a weak magnetic field generated in it's core.  Mercury also has a very large core, but it's only large relative to the planet.  It's not larger than Venus's core, in fact it's not even close.  Venus' core is larger than Mercury.
https://www.newscientist.com/article/2276218-weve-measured-the-size-of-venuss-planetary-core-for-the-first-time/
Mars no longer has an internally generated magnetic field, but surface magnetism indicates that it once had a magnetic field.
Ganymede, the moon of Jupiter has a significantly smaller metalic core and it has a magnetic field of similar strength to Mercury.
https://en.wikipedia.org/wiki/Ganymede_(moon)#Magnetosphere
A circulating core seems essential for a core based magnetic field.  A fast or slow rotation may play a role in that, but it's hard to say how important rotation speed is because it's not really known.  Tidal forces may also have an effect.   Ganymede experiences tidal forces between Jupiter and the outer moons.   Mercury experiences tidal forces due to it's eccentric orbit and Earth does because of the Moon.
What I've read on this subject, the answer is that we don't know exactly what circumstances generate an internal planetary magnetic field beyond circulation within the core.
