Question

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

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

Answer 1

Answer: (A)

Using formula $B=\frac{{\mu }_{0}i{R}^2}{2{\left(R^2+X^2\right)}^{3/2}}$, we get
$54=\frac{{\mu }_{0}i{\left(3\right)}^2}{2{\left[{\left(3\right)}^2+{\left(4\right)}^2\right]}^{3/2}}$
At the centre of the coil, $X=0$ and $B=\frac{{\mu }_{0}i}{2\left(3\right)}$
Using equation $\left(i\right)$
$B=\frac{54\times 5^3}{{\left(3\right)}^2\times 3}\Rightarrow B=250\mu T.$