Question

What would be the change in tangential velocity of an electron, if it remains in same orbit and electronic charge is doubled


Hint:if v is proportional to square root of charge

Answer 1

Answer:

$(\sqrt{2}-1)v$

Explanation:

1) We know that,

Columbic force which provides centripetal acceleration to the electron is proportional to charge q of moving particle. (Here electron )

And centripetal acceleration is proportional to square of its velocity.

2) Moving swiftly to equations, we get

$F_c \propto q\\ \\=>v^2 \propto q \\ =>v \propto \sqrt{q}$

3) If charge gets doubled,

Then,

We have, v_i = initial tangential velocity

v_f = final tangential velocity

$\frac{v_f}{v_i}=\frac{\sqrt{2q}}{\sqrt{q}}\\ \\=>v_f = \sqrt{2}v_i$

Change in tangential velocity,

$\Delta v=v_f-v_i\\ \\ =(\sqrt{2}-1)v_i$