Question

There is a naturally occurring vertical electric field near the Earth's surface that points toward the ground. In fair weather conditions, in an open field, the strength of this electric field is 90.0 N/C. A spherical pollen grain with a radius of 15.0μm is released from its parent plant by a light breeze, giving it a net charge of −0.650fC (where 1fC=1×10−15C ). What is the ratio of the magnitudes of the electric force to the gravitational force, Felectric /Fgrav , acting on the pollen? Pollen is primarily water, so assume that its volume mass density is 1000 kg/m3, identical to the volume mass density of water.

Answer 1

To determine the ratio of the electrical force to the gravitational force acting on a charged pollen grain, we first calculate each force separately. The electrical force is found to be -58.5 × 10^-15 N, while the gravitational force comes out to be 1.38 × 10^-7 N. Thus, the ratio of these forces is -4.24 × 10^-8, showing that the gravitational force greatly outweighs the electrical force.

Step-by-step explanation:

The subject of the question falls under the realm of Physics, specifically the field of Electrostatics and Gravity. First, let's calculate the electric force that the pollen feels. The electric force (Fe) on a charged particle is given by the formula Fe = qE, where q is the charge of the particle and E is the electric field strength. Therefore, Fe = (-0.650 × 10^-15 C) * (90.0 N/C) = -58.5 × 10^-15 N. Note that the negative sign indicates that the force is downward, in the same direction as the electric field.

Next, let's calculate the gravitational force that the pollen feels. First, we need to calculate the mass of the pollen grain. Using the volume of a sphere formula (V = 4/3 * π * r^3) with the given radius, we find that the volume of the pollen grain is 1.41 × 10^-11 m^3. Given a density of 1000 kg/m^3, this gives a mass of 1.41 × 10^-8 kg. The gravitational force (Fg) is given by the formula Fg = mg, where m is the mass and g is the acceleration due to gravity (about 9.81 m/s^2 on the surface of the Earth). Therefore, Fg = (1.41 × 10^-8 kg)*(9.81 m/s^2) = 1.38 × 10^-7 N.

Finally, the ratio of the magnitudes of the electric force to the gravitational force, Felectric /Fgrav, on the pollen grain is then (-58.5 × 10^-15 N)/(1.38 × 10^-7 N) = -4.24 × 10^-8. Thus, the gravitational force is tremendously larger than the electrical force acting on the pollen grain, and effectively, the electric force can be neglected in this system.

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