Honeybees acquire a charge while flying due to friction with the air. A 100 mg bee with a charge of 33 pC experiences an electric force in the earth's electric field, which is typically 100 N/C, directed downward. 1. What is the ratio of the electric force on the bee to the bee's weight?
2. What electric field strength would allow the bee to hang suspended in the air?
3. What electric field direction would allow the bee to hang suspended in the air?

A) 3.367 × 10^(-6)

B) 2.97 × 10^(7) N/C

C) Upwards

Explanation:

We are given;

Mass of bee; m = 100 mg = 100 × 10^(-6) kg

Charge on bee;q=33 pC = 33 × 10^(-12)C

Electric field strength; E = 100 N/C

A) Formula for weight of bee; W = mg = 100 × 10^(-6) × 9.8 = 9.8 × 10^(-4) N

Electric force on Bee; F = qE = 33 × 10^(-12) × 100 = 33 × 10^(-10) N

ratio of the electric force on the bee to the bee's weight; F/W = (33 × 10^(-10))/(9.8 × 10^(-4)) = 3.367 × 10^(-6)

B) For the bee to be suspended in the air, it means the weight of the bee must be equal to the electric force. Thus;

mg = qE

100 × 10^(-6) × 9.8 = 33 × 10^(-12) × E

E = (100 × 10^(-6) × 9.8)/(33 × 10^(-12))

E = 2.97 × 10^(7) N/C

C) From Newton's law, sum of forces = 0.

Thus;

F_n + F + W = 0

Where F is the normal force.

Thus;

F_n = -(F + W)

F_n = - ((33 × 10^(-10)) + (9.8 × 10^(-4)))

F_n = -9.8 × 10^(-4) N

Thus, applied electric field is;

E_a = F_n/q = (-9.8 × 10^(-4))/(33 × 10^(-12)) = -2.97 × 10^(7) N/C

This is negative and so it means the direction will be opposite the Earth's electric filed which is upwards.