I'm currently studying Method of Images in Griffiths book and in section 3.2 he introduces the method of images for a point charge at a distance $d$ from a grounded conducting plane at potential $V = 0$. In subsection 3.2.3, Griffiths compute the energy of the real system and the image charge system and obtain results differing by a factor of 2, The explanation of griffiths is that in the image problem, we do work on both charges bringing them from infinity to a distance $2d$ apart from each other. However in the real problem, griffiths says that we do work only on the point charge $q$, since the induced charge on the conductor moves along an equipotential. My problem is: if the potential inside the grounded conductor still $V=0$ even with the external electric field due to the point charge, how charges can be induced, since no force acts on them? I've tried to re-read conductors section in griffiths chapter 2, but as long as I remember, he makes no mention to this problem.
I've already read some questions related to this topic but none of them answered my question\
Also sorry for possible typos, I'm still learning english