Question

The electron with charge $q=1.6\times {10}^{-19}C$ moves in as orbit of radius $5\times {10}^{-11}$ m with a speed of $2.2\times {10}^{6}m{s}^{-1}$ around an atom.The equivalent current is

• A. $1.12\times {10}^{-6}A$
• B. $1.12\times {10}^{-3}A$
• C. $1.12\times {10}^{-9}A$
• D. 1.12 A

Answer 1

The correct option is B $1.12\times {10}^{-3}A$

Given: The electron with charge $q=1.6\times {10}^{-19}C$ moves in as orbit of radius $5\times {10}^{-11}m$ with a speed of $2.2\times {10}^{6}m{s}^{-1}$ around an atom

To find the equivalent current

Solution:

Current = charge flowing per unit time = charge times the angular frequency

It reduces to the following formula

$I=\frac{q\nu }{2\pi r}$

Substituting the values in the above formula yields

$I=\frac{1.6\times {10}^{-19}\times 2.2\times {10}^6}{2\times 3.14\times 5\times {10}^{-11}}⟹I=\frac{3.52\times {10}^{-13}}{31.4\times {10}^{-11}}⟹I=0.112\times {10}^{-2}⟹I=1.12mA$

is the required equivalent current.