A positive ion $A$ and a negative ion $B$ has charges $6.67 imes10^{-19}$ C and $9.6 imes10^{-10}$ C, and masses $19.2 imes10^{-27}$ kg and $9 imes10^{-27}$ kg respectively. At that instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $P imes10^{45}$, where the value of $10P$ is ______ (Take $\frac1{4\pi\varepsilon_0}=9 imes10^9\ \mathrm{Nm^2C^{-2}}$ and universal gravitational constant as $6.67 imes10^{-11}\ \mathrm{Nm^2kg^{-2}}$) Assume that charge may not be an integral multiple of electrons.

Question

A positive ion $A$ and a negative ion $B$ has charges $6.67	imes10^{-19}$ C and $9.6	imes10^{-10}$ C, and masses $19.2	imes10^{-27}$ kg and $9	imes10^{-27}$ kg respectively. At that instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $P	imes10^{45}$, where the value of $10P$ is ______ (Take $\frac1{4\pi\varepsilon_0}=9	imes10^9\ \mathrm{Nm^2C^{-2}}$ and universal gravitational constant as $6.67	imes10^{-11}\ \mathrm{Nm^2kg^{-2}}$) Assume that charge may not be an integral multiple of electrons.

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $\frac{F_e}{F_g}=\frac{kq_1q_2}{Gm_1m_2}=\frac{9	imes10^9	imes6.67	imes10^{-19}	imes9.6	imes10^{-10}}{6.67	imes10^{-11}	imes19.2	imes10^{-27}	imes9	imes10^{-27}}=5	imes10^{44}=0.5	imes10^{45}$. So $P=0.5$ and $10P=5$. Answer: 5.

Explanation

Reviewed by Dr. Abubacker

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