TS EAMCET · Physics · Electrostatics

An electron is released from a distance of $4 m$ from a stationary point charge $20 nC$ . What will be the speed of the electron when it is $2 m$ away from the point charge?
[Charge of electron $= 1.6 \times 10^{- 19} C$ , mass of electron $= 9 \times 10^{- 31} kg$ , $\frac{1}{4 π ε_{0}} = 9 \times 10^{9}$ S.I. unit]

A $2 \times 10^{6} m s^{- 1}$
B $4 \times 10^{6} m s^{- 1}$
C $1.6 \times 10^{6} m s^{- 1}$
D $2.4 \times 10^{6} m s^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(B) $4 \times 10^{6} m s^{- 1}$

Step-by-step Solution

Detailed explanation

Potential energy of two charged particles separated by distance r is given by, U=14πε0q1q2r. Applying conservation of mechanical energy, ∆U+∆K=0⇒Ui-Uf=12mv2⇒-qe4πε01rf-1ri=12mv2⇒v=29×10-31×20×10-9×1.6×10-1…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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An electron is released from a distance of 4 m from a stationary point charge 20 nC. What will be the speed of the electron when it is 2 m away from the point charge?[Charge of electron =1.6×10-19C, mass of electron =9×10-31 kg, 14πε0=9×109 S.I. unit]

Step-by-step Solution