Question

The magnetic field due to a current carrying circular loop of radius $3cm$ at a point on the axis at a distance $4cm$ from the centre is $54\mu T$. What will magnetic field at the centre of the loop?

• A. $250\mu T$
• B. $125\mu T$
• C. $75\mu T$
• D. $150\mu T$

Answer 1

The correct option is A $250\mu T$

Magnetic field at a distance $x$ from the centre of the coil of radius R and carrying a current $I$ is
$B=\frac{{\mu }_{0}I{R}^2}{2(R^2+x^2{)}^{3/2}}\dots \left(1\right)$

Magnetic field at the current of the coil is $(\therefore x=0)$
$B_0=\frac{{\mu }_{0}I}{2R}\dots \left(2\right)$

Dividing (2) by (1) we get
$\frac{B_0}{B}=\frac{(R^2+x^2{)}^{3/2}}{R^3}\dots \left(3\right)$

Given $B=54\mu T$
$R=3cm=3\times {10}^{-2}m$ and $x=4cm=4\times {10}^{-2}m$

Substituting these values in equation (3) we get,

$B_0=250\mu T$