Question

The magnitude of the force vector acting on a unit length of a thin wire carrying a current $I=8A$ at a point $O$, if the wire is bent as shown in the figure with a radius, $R=10\pi cm$ is

• A. $64\mu N/m$
• B. $32\mu N/m$
• C. $20\mu N/m$
• D. $100\mu N/m$

Answer 1

Answer: (A)

Given, current flowing through wire, $I=8A$
and radius of circular wire,
$R=10\pi cm=10\pi \times 10^{-2}m$
According to the question,

$\because$ Magnetic field produced by semi-circular current carrying thin wire at centre $O$.
$B=\frac{{\mu }_{0}I}{4R}$
Putting the given values, we get
$\Rightarrow B=\frac{4\pi \times 10^{-7}\times 8}{4\times 10\pi \times 10^{-2}}$
$B=8\times 10^{-6}T$
$\therefore$ Magnitude of the force on thin wire per unit length.
$F=IB$
Putting the given values,
$=8\times 8\times 10^{-6}$
$=64\times 10^{-6}N/m=64\mu N/m$