Only try this at home
Do you ever embark on something on the board and suddenly wish you hadn't? Today I did. I was doing about the gravitational field around two spherical masses and for some reason decided to draw the variation of field as you tunnel through each sphere. Quickly abandoned the idea and plotted potential which, being a scalar, was much easier. Anyway I had a think about the field problem and it is quite difficult because as you tunnel through one sphere the field strength will have two components one from the inner sphere of the one you're tunnelling through and one from the other sphere. So when in the middle there is no component from the one you're in but you are still attracted to the other one as you moved through the hole towards the other mass you'd reach a point, before getting out of the hole where the field was zero. Then when you got out of the hole and travelled towards the other mass there would be a second zero. Maybe. Very confusing so I made it in Algodoo. A nice way to show the field by dropping balls all over. Doesn't give the expected result though. Good job I didn't show this in class.