Name: Dielectrics in a Capacitor
Uploaded: 2019-07-19
Duration: 6 min 3 s
Description: Let us use our knowledge about dielectrics and capacitors to find out how the use of dielectrics can increase the capacitance of a system. Learn through this...

Question

Calculate the ratio of the electrostatic to gravitational interaction forces between two electrons, between two protons. At what value of the specific charge

\frac{q}{m}

of a particle would these forces become equal (in their absolute values) in the case of interaction of identical particles?

Accepted Answer

The electrostatic force between two point charges is given by Coulomb's law as,

$F_{E} = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r^{2}}$

And the gravitational force between two point masses is given by Newton's universal law of gravitation as,

$F_{G} = \frac{G m_{1} m_{2}}{r^{2}}$

For two electrons,

$F_{E} = \frac{e^{2}}{4 π ε_{0} r^{2}}$ and $F_{G} = \frac{G {m_{e}}^{2}}{r^{2}}$

$\Rightarrow \frac{F_{E}}{F_{G}} = \frac{e^{2}}{4 π ε_{0} G {m_{e}}^{2}}$

where, $e = 1.602 \times 10^{- 19} C$

$G = 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}$

$\frac{1}{4 π ε_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}$

$m_{e} = 9.11 \times 10^{- 31} kg$

$\Rightarrow \frac{F_{E}}{F_{G}} = \frac{{(1.602 \times 10^{- 19})}^{2}}{(\frac{1}{9 \times 10^{9}}) \times (6.67 \times 10^{- 11}) \times {(9.11 \times 10^{- 31})}^{2}} \approx 4 \times 10^{42}$

Similarly, for two protons,

$\frac{F_{E}}{F_{G}} = \frac{e^{2}}{4 π ε_{0} G {m_{p}}^{2}}$

where, $m_{p} = 1.672 \times 10^{- 27} kg$

$\frac{F_{E}}{F_{G}} = \frac{{(1.602 \times 10^{- 19})}^{2}}{(\frac{1}{9 \times 10^{9}}) \times (6.67 \times 10^{- 11}) \times {(1.672 \times 10^{- 27})}^{2}} \approx 1 \times 10^{36}$

For the electrostatic interaction to be equal in magnitude to the gravitational interaction, we have,

$F_{E} = F_{G}$

$\frac{q^{2}}{4 π ε_{0} r^{2}} = \frac{G m^{2}}{r^{2}}$

$\Rightarrow \frac{q}{m} = \sqrt{4 π ε_{0} G}$

$\Rightarrow \frac{q}{m} = \sqrt{\frac{6.67 \times 10^{- 11}}{9 \times 10^{9}}} = 0.86 \times 10^{- 10} C {kg}^{- 1}$

Calculate the ratio of the electrostatic to gravitational interaction forces between two electrons, between two protons. At what value of the specific charge $\frac{q}{m}$ of a particle would these forces become equal (in their absolute values) in the case of interaction of identical particles?

Important Questions on ELECTRODYNAMICS

Learn and Prepare for any exam you want !

Calculate the ratio of the electrostatic to gravitational interaction forces between two electrons, between two protons. At what value of the specific charge qm of a particle would these forces become equal (in their absolute values) in the case of interaction of identical particles?

Important Questions on ELECTRODYNAMICS

Learn and Prepare for any exam you want !

Calculate the ratio of the electrostatic to gravitational interaction forces between two electrons, between two protons. At what value of the specific charge $\frac{q}{m}$ of a particle would these forces become equal (in their absolute values) in the case of interaction of identical particles?