Assume that a honeybee is a sphere of diameter 1.004 cm with a charge of +48.3 p

Question

Assume that a honeybee is a sphere of diameter 1.004 cm with a charge of +48.3 pC uniformly spread over its surface. Assume also that a spherical pollen grain of diameter 43.3 m is electrically held on the surface of the honeybee because the bee's charge induces a charge of -1.02 pC on the near side of the grain and a charge of +1.02 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 1.011 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 -48.3 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?

Explanation / Answer

diameter of honeybee, D = 1.004 cm = 0.01004 m

charge , q = 48.3 pC = 48.3*10^-12 C

diameter pf pollengrain, d = 43.3 micro m

chaqrge induced due on pollen, Q = 1.02 pC on far side, -Q on near side

charge on stigma q' = -48.3 pC

dsistance from stigma to nearest point of the grain D' = 1.011*10^-3 m

a. Magnitude of net electrostatic forc eon the bee = 4kQq[1/(D + 2d)^2 - 4/D^2]

F = 8.98*10^9*48.3*10^-12*1.02*10^-12 [ 1/(0.01004 + 2*43.4*10^-6)^2 - 1/(0.01004)^2] *4 = -2.99*10^-10 N

b. Magnitude of net electrostatic forc eon the grainm due to stigma = 4kQq'[1/(D' + 2d)^2 - 4/D'^2]

F = 8.98*10^9*48.3*10^-12*1.02*10^-12 [ 1/(0.001011 + 2*43.4*10^-6)^2 - 1/(0.001011)^2] *4 = -1.729*10^-6 N

c. the force on the grain from the stigmas is more than the force from the bee, andf bnoth force are attreactive in nature

so the pollenm grain goes to the stigma

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