Difference in work done to move magnet

[akashverma]

If a neodymium magnet sticks over a steel plate and you want to separate them, it is advised to apply force such that the magnet slips over steel plate.
So I was just wondering what would be the quantified decrement of this force as compared to the case when force is applied axially to separate them.

 

[CWatters]

Force or work?

I believe the work should be the same in both cases. The force might be lower when sliding the magnet off the edge of the metal. I don't fancy doing the maths but I think there is an analogy with climbing a hill. The hill has a fixed height so as far as work is concerned it should be the same whatever route you take up the hill. However if you zig zag back and forth as you go up the force would be lower than taking the direct route to the top.

 

[akashverma]

When climbing a hill work done remains constant as we do work against gravity which is a conservative force and for conservative forces work done doesn't depends on path but depends on displacement which is same for both steep climbing and zig-zag climbing.
In this case Force is different which is evident from the smoothness in separating metal and magnet through sliding and also the displacement in both the cases would be different in direction which gives different work done.
And my question is to find out a quantitative difference between these two processes.