Question

the charges on several spheres are shown. which spheres are negatively-charged? (note that there are 8 individual charge signs on each sphere.) include all that apply.

Explanation:

Step1: Count negative charges

For sphere A: count the number of “-” signs. There are 8 “-” signs.
For sphere B: count the number of “-” signs. There are 0 “-” signs.
For sphere C: count the number of “-” signs. There are 3 “-” signs.
For sphere D: count the number of “-” signs. There are 5 “-” signs.
For sphere E: count the number of “-” signs. There are 3 “-” signs.
For sphere F: count the number of “-” signs. There are 2 “-” signs.
For sphere G: count the number of “-” signs. There are 1 “-” sign.
For sphere H: count the number of “-” signs. There are 4 “-” signs.

Step2: Determine negative - charged spheres

A sphere is negatively - charged if the number of “-” signs is greater than the number of “+” signs.
Since each sphere has 8 charge signs in total. If \(n_{-}>n_{+}\) (where \(n_{-}\) is the number of negative charges and \(n_{+}\) is the number of positive charges, and \(n_{-}+n_{+} = 8\)), then \(n_{-}>4\)
Only sphere A (\(n_{-}=8\)) and sphere D (\(n_{-}=5\)) have \(n_{-}>4\)

Answer:

A. Sphere A, D.