What is causing my battery light to turn on and off?

What is your question?

Battery light keeps coming up ..just bought new battery and issue continues. The steering wheel gets very stiff. The radiator has been checked and it's working fine. The battery light tends to only come up when making a deep turn or backing up. What can be causing this?

What makes this problem better or worse?

It's worse when backing up or making a turn.

How long has your 2006 Hyundai Elantra had this problem?

A month?