What might happen to the magma convection currents if there were no radiogenic heat produced in the core? How would this affect life on Earth?

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If there were no radiogenic heat produced in the core, there would be no convection currents, and life on the Earth would not be possible.

Explanation:

The convection currents are the result of heating by temperature gradients. Differences in temperature and density produce these currents. Warm materials are lighter and can ascend, while cold materials are heavier and denser, so they tend to descend. These materials movements create a circular motion pattern known as convective currents. They occur in the atmosphere, in the water, and the Earth mantle. In the last case, while the hot material emerges from the bottom areas, the cold mantle sinks, creating a circular convection current. These play a significant role in fluids circulation and might be responsible for the movements of the lithospheric plates that are over the mantle. The temperature on the surface is much inferior that the mantle´s temperature, so the lithospheric pieces sink, creating a descendent current. Near the terrestrial core, the heat might reach up to 3,500ºC, and solid materials in these areas melt and fuse. When fusing, materials lose density, becoming lighter and ascending again to the surface, creating the ascending currents. The currents of ascending materials are known as thermal feathers or plumes.

Hot ascending material keeps the surface warm, making life possible. Also, radiogenic heat produced in the core is responsible for the electromagnetic field.

The electromagnetic field protects the Earth from many particles that come forward to the surface from space, specifically from the sun. The electromagnetic field also influences the atmosphere, keeping it in its place, necessary for life on Earth.

The plate´s movement produces earthquakes and volcanic activity. Both of them also necessary for many reasons, such as keeping fertile soils and producing necessary atmospheric gasses.

Through the years, the core losses heat, and eventually, it will become solid. When this happens, convective currents will stop because there will be no heat from the bottom to make them move. The electromagnetic field will disappear, and the atmosphere will be affected as well. The Earth surface will become cold. Mantle movement will stop, and there will be no earthquakes nor volcanic activities. Every living being on Earth will be affected by this fact. Life on Earth will not be possible.