Question

A long straight wire carries a current $i=2\text{A}$. A particle having a positive charge $q=1\text{C}$ and mass $5\text{mg}$, kept at a distance $x_0=5\text{cm}$ from the wire is projected towards it with a speed $v=20\text{cm/s}$. Find the minimum separation between the wire and the particle.

• A. $10\text{mm}$
• B. $20\text{mm}$
• C. $14.3\text{mm}$
• D. $17.6\text{mm}$

Answer 1

The correct option is C $14.3\text{mm}$

Minimum separation between the wire and particle is given by $$x_{min}=x_0{e}^{-\frac{2\pi mv}{{\mu }_{0}qi}}$$From the data given in the question,

$x_{min}=5\times {10}^{-2}\times e^{-\frac{2\pi \times 5\times {10}^{-6}\times 20\times {10}^{-2}}{4\pi \times {10}^{-7}\times 1\times 2}}$

$\Rightarrow x_{min}=5\times {10}^{-2}\times 0.28$

$\Rightarrow x_{min}=14.3\text{mm}$

Hence, option (c) is the correct answer.