Question

A charge $q$ at a distance $x$ from straight current carrying wire is moving towards it with speed $v$, experiences a magnetic force of magnitude $F$. If the distance of the charge from the wire is $2 x$ (all other conditions remaining the same) then the force would be

• A. $F$
• B. $2 F$
• C. $\frac{F}{2}$
• D. $\frac{F}{4}$

Answer 1

Answer: (C)

Magnetic force, $F=q v B, $
$\therefore F \propto B$
Magnetic field at a point distant ' $x$ ' due to a straight conductor carrying current is
$F=\frac{\mu_{0}}{4 \pi} \frac{2 I }{ x } $
$ \therefore F \propto \frac{1}{x}$
$\therefore B \propto \frac{1}{ x }$