Simple equation to show work done on an equipotential surface is zero

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w = ΔKE + ΔPE

For a particle moving at constant speed, there is no change in velocity so no change in KE. What about change in PE for a partcile moving at constant speed on a equipotential surface? Would I be right in stating that since the particle moves along the same surface (AKA same height), there is no change in height and therefore no change in PE?
 
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Yes.You are correct.
 
I don't think I would phrase it in terms of "height". There are many ways of having potential energy that have nothing to do with height. As long as the object is moving on an "equipotential surface", its potential energy doesn't change- by definition of "equipotential".
 

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