Check that the ratio $ke ^{2} / G m _{ e } m _{ p }$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?
Check that the ratio $ke ^{2} / G m _{ e } m _{ p }$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?
The given ratio is $\frac{k e^{2}}{G m_{e} m_{p}} .$ Where, $G=$ Gravitational constant. Its unit is $N m ^{2} \,kg ^{-2}$
$m _{ c }$ and $m _{ p }=$ Masses of electron and proton and their unit is kg.
$e =$ Electric charge. Its unit is $C$. $k=\frac{1}{4 \pi \varepsilon_{0}}$ and its unit is $N m ^{2} \,C ^{-2}$
Therefore, unit of the given ratio
$\frac{k e^{2}}{G m_{e} m_{p}}=\frac{\left[N m^{2} C^{-2}\right]\left[C^{-2}\right]}{\left[N\, m^{2}\, k g^{-2}\right][k g][k g]}$$=M^{0} L^{0} T^{0}$
Hence, the given ratio is dimensionless. $e=1.6 \times 10^{-19} \,C$
$G=6.67 \times 10^{-11}\, N m ^{2}\, kg ^{-2}$
$m _{ e }=9.1 \times 10^{-31} \,kg$
$m _{ p }=1.66 \times 10^{-27}\, kg$
Hence, the numerical value of the given ratio is
$\frac{k e^{2}}{G m_{e} m_{p}}=\frac{9 \times 10^{9} \times\left(1.6 \times 10^{-19}\right)^{2}}{6.67 \times 10^{-11} \times 9.1 \times 10^{-31} \times 1.67 \times 10^{-27}}$$\approx 2.3 \times 10^{39}$
This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.
Similar Questions
A charge $q$ is placed in the middle of a line joining the two equal and like point charge $Q$. This charge $q$ will remain in equilibrium for which value of $q$ is
A charge $q$ is placed in the middle of a line joining the two equal and like point charge $Q$. This charge $q$ will remain in equilibrium for which value of $q$ is
Two similar spheres having $ + \,q$ and $ - \,q$ charge are kept at a certain distance. $F$ force acts between the two. If in the middle of two spheres, another similar sphere having $ + \,q$ charge is kept, then it experience a force in magnitude and direction as
Two similar spheres having $ + \,q$ and $ - \,q$ charge are kept at a certain distance. $F$ force acts between the two. If in the middle of two spheres, another similar sphere having $ + \,q$ charge is kept, then it experience a force in magnitude and direction as
Positive point charges are placed at the vertices of a star shape as shown in the figure. Direction of the electrostatic force on a negative point charge at the centre $O$ of the star is
Positive point charges are placed at the vertices of a star shape as shown in the figure. Direction of the electrostatic force on a negative point charge at the centre $O$ of the star is
- [KVPY 2017]
An isolated solid metallic sphere is given $ + Q$ charge. The charge will be distributed on the sphere
An isolated solid metallic sphere is given $ + Q$ charge. The charge will be distributed on the sphere
The diagrams depict four different charge distributions. All the charged particles are at same distance from origin $(i.e. OA = OB = OC = OD)$ $F_1$ , $F_2$ , $F_3$ and $F_4$ are the magnitude of electrostatic force experienced by a point charge $q_0$ kept at origin in figure $-1$ , figure $-2$ , figure $-3$ and figure $-4$ respectively. Choose the correct statement.
The diagrams depict four different charge distributions. All the charged particles are at same distance from origin $(i.e. OA = OB = OC = OD)$ $F_1$ , $F_2$ , $F_3$ and $F_4$ are the magnitude of electrostatic force experienced by a point charge $q_0$ kept at origin in figure $-1$ , figure $-2$ , figure $-3$ and figure $-4$ respectively. Choose the correct statement.