Assume that a honeybee is a sphere of diameter 1.026 cm with a charge of +45.7 p

Question

Assume that a honeybee is a sphere of diameter 1.026 cm with a charge of +45.7 pC uniformly spread over its surface. Assume also that a spherical pollen grain of diameter 42.4 mu m is electrically held on the surface of the honeybee because the bee's charge induces a charge of -1.01 pC on the near side of the grain and a charge of +1.01 pC on the far side, (a) What is the magnitude of the net electrostatic force on the grain due to the bee? Next, assume that the bee brings the grain to a distance of 1.021 mm from the tip of a flower's stigma (it is a distance between the tip of stigma and nearest point of the grain surface) and that the tip is a particle of charge -45.7 pC. (b) What is the magnitude of the net electrostatic force on the grain due to the stigma? (c) Does the grain remain on the bee or does it move to the stigma? (a) Number Units (b) Number Units (c)

Explanation / Answer

given, honeybee is a sphere of diameter, d = 1.026 cm

charge Q = 45.7 pC

diameter of pollen grain, D = 42.4 micro m

q = -1.01 pc on near sider and +1.01 pC on the far side of pollen grain

a. Net force on pollen grain = F = kQq[1/(d/2)^2 - 1/(d/2 + D)^2] = k45.7*1.01*10^-24[1/0.00513^2 - 1/(0.0051724)^2] = 2.597*10^-10 N

b. distance from stigma, r = 1.021 mm

charge on stigma = -Q

so force due to stigma, F' = kQq[1/(r - D/2)^2 - 1/(r + D/2)^2] = 3.066*10^-8 N

c. so net force by stigma is greater so the pollen goes to the stigma and leaves rthe bee

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