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Question: a charged cloud system Produces an electric field in the air near the Earth's surface A particle of ...

a charged cloud system Produces an electric field in the air near the Earth's surface A particle of charge −2×10−9 - 2 \times {10^{ - 9}} coulomb is acted on by a downward electrostatic force of 3×10−63 \times {10^{ - 6}} Newton when placed in this field the gravitational and electrostatic force respectively exerted on a Proton placed in this field.

Explanation

Solution

Hint
Here, we have to find the value of electrostatic force exerted on the proton which is the product of proton charge and electric field i.e. Fe=qE{F_e} = qE, as the charge ion proton is q=1.6×10−19Cq = 1.6 \times {10^{ - 19}}C now we have to find the electric field, for this the charge and electrostatic force is given we can easily find the value of electric field. For gravitational force the formula is Fg=mg{F_g} = mg, m is mass of proton i.e. m=1.67×10−27kgm = 1.67 \times {10^{ - 27}}kg and g is acceleration due to gravity i.e. g=9.8ms−2g = 9.8m{s^{ - 2}}

Complete step by step answer
It is given that the charge particle of charge −2×10−9 - 2 \times {10^{ - 9}}coulomb is acted upon by the electrostatic force i.e. 3×10−63 \times {10^{ - 6}}Newton. We can find the electric field by using the formula.
Electric force is the product of charge and electric field acting on that charge, therefore
Electric field is E=FqE = \dfrac{F}{q}
Substitute the value of F and q, we get
⇒E=3×10−62×10−9=1.5×103NC−1\Rightarrow E = \dfrac{{3 \times {{10}^{ - 6}}}}{{2 \times {{10}^{ - 9}}}} = 1.5 \times {10^3}N{C^{ - 1}}
Now, we have to find the value of electrostatic force exerted on the proton due to the electric field E.
We again use the formula that electrostatic force is the product of electric field and charge i.e. F=qEF = qE, q is the charge of proton and E is the electric field
On substituting the values, we get
⇒F=1.67×10−27×1.5×103\Rightarrow F = 1.67 \times {10^{ - 27}} \times 1.5 \times {10^3}
⇒F=2.4×10−16N\Rightarrow F = 2.4 \times {10^{ - 16}}N
This is the required electrostatic force acting on the proton.
Now, gravitational force acting on the proton is the product of the mass of proton and acceleration due to gravity that is
, m is the mass of proton i.e. m=1.67×10−27kgm = 1.67 \times {10^{ - 27}}kg
g is the acceleration due to gravity i.e. g=9.8ms−2g = 9.8m{s^{ - 2}}
on substituting the values, we get
⇒Fg=1.67×10−27×9.8\Rightarrow {F_g} = 1.67 \times {10^{ - 27}} \times 9.8
⇒Fg=15.68×10−27N\Rightarrow {F_g} = 15.68 \times {10^{ - 27}}N
This is the required value of the gravitational force exerted on the proton.

Note
Gravitational force is the force which is proportional to the masses of the objects and Electrostatic forces is the force which is directly proportional to the product of charges, it is the same as that of coulomb’s forces. Electrostatic forces are more dominant than gravitational forces.