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

Answer: (A)

$250\, \mu T$

Answer 2

Using formula $B = \frac{\mu_{0}iR^{2}}{2\left(R^{2}+X^{2}\right)^{3/2}}$, 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 $\left(i\right)$ $B = \frac{54\times5^{3}}{\left(3\right)^{2}\times3} \Rightarrow B = 250\,\mu T.$