Question

The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance $\frac{r}{2}$ from the centre is :

• A. $\frac{B}{2}$
• B. 2B
• C. $(\frac{2}{\sqrt5})^{3B}$
• D. $(\frac{2}{\sqrt3})^{3B}$

Answer 1

Answer: (C)

$(\frac{2}{\sqrt5})^{3B}$

Answer 2

B=$\frac{μ_0l}{2r}$
$B_a$=$\frac{μ_0lr^2}{2(r^2+\frac{r}{4})}$
⇒$\frac{B_a}{B}$=($\frac{2}{\sqrt5}$)3
⇒$B_a$=($\frac{2}{\sqrt5}$)3B

The correct option is (C) : $(\frac{2}{\sqrt5})^{3B}$