Question

Derive an expression for the displacement produced when an electric field acts parallel to electron motion

Answer 1

Derivation:

Assumptions:

• Let's assume that electrostatic field intensity of E is acting parallel to the electron motion.

• The electron is initially at rest.

• Displacement after time t be 'd'.

Calculation:

Force on the electron (inside the field) be F.

$\sf \: F =q \times E$

$\sf \implies\: F =e \times E$

$\sf \implies\: F =e E$

$\sf \implies\: a = \dfrac{e E}{m}$

Now, since acceleration is constant, the displacement can be calculated from NEWTON'S EQUATION OF KINEMATICS:

$\sf \: d = ut + \dfrac{1}{2} a {t}^{2}$

$\sf \implies\: d = (0)t +( \dfrac{1}{2} \times \dfrac{eE}{m} \times {t}^{2} )$

$\sf \implies\: d = \dfrac{eE {t}^{2} }{2m}$

So, final answer is:

$\boxed{ \bold{\: d = \dfrac{eE {t}^{2} }{2m} }}$