Question

The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm 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

The correct option is A 250 $\mu T$

$\text{Magnetic field at the center of a current carrying loop of radius}r\text{is given by,}$

$B=\frac{{\mu }_{0}nI}{2r}$

$\text{Magnetic field along the axis of a current carrying loop of radius}r\text{at a distance}$

$x\text{from the center is given by,}$

$B_x=\frac{{\mu }_{0}nI}{2}\frac{r^2}{{(x^2+r^2)}^{3/2}}$

$B_x=\frac{{\mu }_{0}nI}{2r}{\left(\frac{r^2}{x^2+r^2}\right)}^{3/2}$

$\text{Thus}\frac{B}{B_x}={\left(\frac{r^2+x^2}{r^2}\right)}^{3/2}$

$\Rightarrow B={\left(\frac{3^2+4^2}{3^2}\right)}^{3/2}\times 54=250\mu \text{T}$