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KCET · Physics · Electrostatics

An electron falls through a distance \(1.5\) cm in \(2.0 \times 10^4\) N/C from rest. The time taken to cover this distance in second is ____
\((e = 1.6 \times 10^{-19}\text{ C}, m_e = 9.11 \times 10^{-31}\text{ kg})\)

  1. A \(2.9 \times 10^{-9}\)
  2. B \(2.9 \times 10^{9}\)
  3. C \(4 \times 10^{-6}\)
  4. D \(4 \times 10^{6}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2.9 \times 10^{-9}\)

Step-by-step Solution

Detailed explanation

Force on the electron is \(F = eE\)

Acceleration of the electron is \(a = \dfrac{eE}{m_e}\)

Using the equation of motion \(s = ut + \dfrac{1}{2}at^2\)

Since the electron starts from rest, \(u = 0\)

\(s = \dfrac{1}{2} \left( \dfrac{eE}{m_e} \right) t^2\)

\(t = \sqrt{\dfrac{2sm_e}{eE}}\)

Substituting the given values:

\(t = \sqrt{\dfrac{2 \times 1.5 \times 10^{-2} \times 9.11 \times 10^{-31}}{1.6 \times 10^{-19} \times 2.0 \times 10^4}}\)

\(t = \sqrt{\dfrac{27.33 \times 10^{-33}}{3.2 \times 10^{-15}}}\)

\(t = \sqrt{8.54 \times 10^{-18}}\)

\(t \approx 2.9 \times 10^{-9} \text{ s}\)

Answer: \(2.9 \times 10^{-9}\)