Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two balls are apart. Find the gravitational potential and field midway between them. How much work takes a body from there to very far away?
Taking zero far away: potential energy , potential . The work to move a body from to is , close to only for heights much smaller than . Near the Earth, .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Potential. .
Step 2. Field. Equal and opposite pulls cancel: .
Step 3. Work. From to : .
Answer: ; zero field; .
Watch out. A point with zero field can still have a potential: here the body is in a 'saddle'.
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