Question

Two long thin conductors $10$ $cm$ apart carry currents in the ratio $1:2$ in the same direction. The magnetic field midway between them is $2\times {10}^{-3}$ Tesla. The force on $1$ metre length of any conductor will be :

• A. $2\pi$ x ${10}^{-3}$ Newton
• B. $2\times {10}^{-3}$ Newton
• C. $\pi$ Newton
• D. $1$ Newton

Answer 1

Answer: (D)

$1$ Newton

Magnetic field at $P=\frac{{\mu }_0}{2\pi (\frac{d}{2})}[2i-i]=\frac{{\mu }_{0}i}{\pi d}$

$\frac{{\mu }_{o}i}{\pi d}=2\times {10}^{-3}$

$i=\frac{2\times {10}^{-3}\times 0.1}{4\times {10}^{-7}}$
or $i=\frac{{10}^3}{2}$

Magnetic field on II due to I = $\frac{{\mu }_{o}i}{2\pi d}=B$
Force on unit length of II $=B\times 2i$
$=\frac{{\mu }_o{i}^2}{\pi d}$
$=1$ Newton