Check that the ratio $\frac{{ke}^{2}}{{Gm}_{e} m_{p}}$ is dimensionless. Look up a table of physical constants and determine the value of this ratio. What does the ratio signify?

Solution

$Electrostatic force is given by F = K \frac{q_{1} q_{2}}{r^{2}} Gravitational force is given by F = G \frac{m_{1} m_{2}}{r^{2}}$
   $where G = 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2} m_{e} = 9.1 \times 10^{- 31} kg m_{p} = 1.67 \times 10^{- 27} kg e = 1.6 \times 10^{- 19} C$
and    $k = \frac{1}{4 {πε}_{0}} = 9 \times 10^{9} \frac{{Nm}^{2}}{C^{2}}$
Now,    $\frac{{ke}^{2}}{{Gm}_{e} m_{p}} = \frac{9 \times 10^{9} \frac{{Nm}^{2}}{C^{2}} \times 1.6 \times 10^{- 19} C \times 1.6 \times 10^{- 19} C}{6.67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2} \times 9.1 \times 10^{- 31} kg \times 1.67 \times 10^{- 27} kg} = 2 \times 27 \times 10^{39} which is dimensionless .$

It also establishes that the electrostatic force is about 10³⁹ times stronger than the gravitational force.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

Check that the ratio $\frac{{ke}^{2}}{{Gm}_{e} m_{p}}$ is dimensionless. Look up a table of physical constants and determine the value of this ratio. What does the ratio signify?

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

Check that the ratio ke2Gmempis dimensionless. Look up a table of physical constants and determine the value of this ratio. What does the ratio signify?

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Check that the ratio $\frac{{ke}^{2}}{{Gm}_{e} m_{p}}$ is dimensionless. Look up a table of physical constants and determine the value of this ratio. What does the ratio signify?

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?