In the uniform electric field of E = 1 × 104 NC -1, an electron is accelerated from rest. The velocity (in m s-1) of the electron when it has travelled a distance of 2 × 10-2 m is nearly ( (e/m)of electron = 1.8 × 1011 C kg-1)

Question

In the uniform electric field of E = 1 × 104 NC -1, an electron is accelerated from rest. The velocity (in m s-1) of the electron when it has travelled a distance of 2 × 10-2 m is nearly ( (e/m)of electron = 1.8 × 1011 C kg-1) (A) 1.6×106 ms-1 (B) 0.85×106 ms-1 (C) 0.425 ×106 ms-1 (D) 8.5 × 106 ms-1

Tardigrade Admin · Accepted Answer

By work-energy theorem, Work done by electric field = Change in KE of electron or qE x=(1/2) m v2 or v =√(2 q E x/m) =√2 × 1.8 × 1011 × 1 × 104 × 2 × 10-2 =8.5 × 106 ms -1

Q. In the uniform electric field of $E = 1 \times 1 0^{4} N C^{- 1}$ , an electron is accelerated from rest. The velocity (in $m s^{- 1})$ of the electron when it has travelled a distance of $2 \times 1 0^{- 2}$ m is nearly $(\frac{e}{m}$ of electron $= 1.8 \times 1 0^{11} C k g^{- 1})$

$1.6 \times 1 0^{6} m s^{- 1}$

$0.85 \times 1 0^{6} m s^{- 1}$

$0.425 \times 1 0^{6} m s^{- 1}$

$8.5 \times 1 0^{6} m s^{- 1}$

By work-energy theorem,
Work done by electric field = Change in KE of electron
or $qE x = \frac{1}{2} m v^{2}$
or $v = \frac{2 qE x}{m}$
$= 2 \times 1.8 \times 1 0^{11} \times 1 \times 1 0^{4} \times 2 \times 1 0^{- 2}$
$= 8.5 \times 1 0^{6} m s^{- 1}$

Q. In the uniform electric field of E=1×104NC−1, an electron is accelerated from rest. The velocity (in ms−1) of the electron when it has travelled a distance of 2×10−2 m is nearly (me​of electron =1.8×1011Ckg−1)

1.6×106ms−1

0.85×106ms−1

0.425×106ms−1

8.5×106ms−1