Two charged bees land simultaneously on flowers that are separated by a finite distance. For a few moments, the charged bees rest on the flowers. The charged bees both generate an electric field, and while the charged bees are resting on the flowers, the net electric field at some distance between them is zero. (a) Do the bees have the same or opposite signs of charge?
Same � the electric fields point in opposite directions and therefore cancel at some midpoint.
Same � the electric fields multiply together to equal zero.
Opposite � the electric fields point in the same direction summing to zero.
Opposite � the net electric field due to the two bees points in a direction perpendicular to the direction from one bee to the other.
(b) Suppose the net electric field is zero at a distance that is closer to bee 1. Does bee 1 have a magnitude of charge greater than or less than that of bee 2?
greater than
less than

a. Same � the electric fields point in opposite directions and therefore cancel at some midpoint.

b. bee 1 has a magnitude of charge less than bee 2

Explanation:

a. Do the bees have the same or opposite signs of charge?

They have the same charge. This is because since same charges would produce electric fields in opposite directions, that is the only way they can cancel out at some point. So, the charges are the same and the electric fields point in opposite directions and therefore cancel at some midpoint.

b. Suppose the net electric field is zero at a distance that is closer to bee 1. Does bee 1 have a magnitude of charge greater than or less than that of bee 2?

Let q be the charge on bee 1 and r its distance from the neutral electric field point. So, it electric field E = kq/r².

Also, let q' be the charge on bee 2 and d its distance from the neutral electric field point. So, it electric field E' = kq'/d².

Since E = E' at the neutral point.

kq/r² = kq'/d²

q/q' = r²/d² = (r/d)²

Given that r < d, so r/d < 1 and (r/d)² < 1

So, q/q' < 1

q < q'

So, the charge on bee 1 is less than that on bee 2  

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