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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 95.0 N/C . A spherical pollen grain with a radius of 15.0 μm is released from its parent plant by a light breeze, giving it a net charge of −0.800 fC (where 1 fC=1×10−15 C ). What is the ratio of the magnitudes of the electric force to the gravitational force, ????electric/????grav , 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.

Respuesta :

Answer:

The ratio of the electric force and the gravitational force is 1.85

Explanation:

Given:

  • The strength of the electric Field E=95 N/C
  • Charge of the pollen grain [tex]Q=15\times10^{-15} \ C[/tex]
  • Density of the pollen grain, [tex]\rho=1000\ \rm kg/m^3[/tex]

Let m be the mass of the pollen grain given  by

[tex]m=\rho \times\dfrac{4\pi R^3}{3}\\m=1000 \times\dfrac{4\pi (15\times10^{-6})^3}{3}\\\\m=4.18\times10^{-15}\ \rm kg[/tex]

Gravitational force acting on the pollen grains

[tex]=mg\\=4.18\times10^{-15}\times9.8\\=40.96 \times10^{-15}\ N[/tex]

The Electric force acting on the pollen grains

[tex]=qE\\=.8\times10^{-15}\times95\\=76\times10^{-15}\ N[/tex]

The ratio of electric force to the gravitational force

=[tex]=\dfrac{76\times10^{-15}}{40\times10^{-15}}\\=1.855[/tex]

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