Question

The earth's magnetic induction at a certain point is $7\times {10}^{-5}Wb{m}^{-2}$. This is to be annulled by the magnetic induction at the centre of a circular conducting loop of radius $15cm$. The required current in the loop is :

• A. $0.56A$
• B. $5.6A$
• C. $0.28A$
• D. $2.8A$

Answer 1

The correct option is B $5.6A$

Magnetic induction due to circular coil at its center is given by $B=\frac{{\mu }_{o}NI}{2R}$
Now this field annuls the earth's magnetic induction therefore, it must be equal to $7\times {10}^{-5}T$
$\frac{{\mu }_{o}NI}{2R}=7\times {10}^{-5}$
$I=\frac{2R\times 7\times {10}^{-5}}{{\mu }_o}$
$I=\frac{0.3\times 7\times {10}^{-5}}{4\pi \times {10}^{-7}}$
$I=5.6A$