Question

The magnetic field $B$ due to a current-carrying circular loop of the radius $12cm$ at its centre is $0.5\times 10^{-4}T$ . The magnetic field due to this loop at a point on the axis at a distance of $5cm$ from the centre -

• A. $3.9\times 10^{-5}T$
• B. $5.2\times 10^{-5}T$
• C. $2.1\times 10^{-5}T$
• D. $9\times 10^{-5}T$

Answer 1

Answer: (A)

$B_0=\frac{{\mu }_{0}I}{2a}$
At axial point
$B=\frac{{\mu }_{0}I{a}^2}{2{\left(a^2+x^2\right)}^{3/2}}$
$\frac{B}{B_0}=\frac{a^3}{{\left(a^2+x^2\right)}^{3/2}}$
$\Rightarrow B=B_0\frac{a^3}{{\left(a^2+x^2\right)}^{3/2}}$
$=0.5\times 10^{-4}\times \frac{(12cm{)}^3}{{\left(144c{m}^2+25c{m}^2\right)}^{3/2}}$
$=3.9\times 10^{-5}T.$