Question

An electron of mass 'm' and charge 'q' is accelerated from rest in a uniform electric field of strength 'E'. The velocity acquired by it as it travels a distance 'l' is

• A. $\left[ \frac{2 Eql}{m} \right]^{1/2}$
• B. $\left[ \frac{2 Eql}{ml} \right]^{1/2}$
• C. $\left[ \frac{2 Eml}{ql} \right]^{1/2}$
• D. $\left[ \frac{Eq}{ml} \right]^{1/2}$

Answer 1

Answer: (A)

$\left[ \frac{2 Eql}{m} \right]^{1/2}$

Answer 2

An electron accelerated from rest by a uniform electric field gains work equal to the kinetic energy.

1. Work done:

   $W = qEl$

2. Kinetic energy:

   $\frac{1}{2}mv^2 = qEl$

3. Solve for $v$:

   $v = \sqrt{\frac{2qEl}{m}}$