Question

$B_X$ and $B_Y$ are the magnetic field at the centre of two coils of two coils $X$ and $Y$ respectively, each carrying equal current. If coil $X$ has $200$ turns and $20\, cm$ radius and coil $Y$ has $400$ turns and $20 \,cm$ radius, the ratio of $B_X$ and $B_Y$ is

• A. $1: 1$
• B. $1: 2$
• C. $2: 1$
• D. $4: 1$

Answer 1

Answer: (B)

At centre $B = N \left(\frac{\mu_0 i }{2 R }\right)$
$ B _{ x }=200\left(\frac{\mu_0 i }{2 \times 20 cm }\right) $
$B _{ y }=400\left(\frac{\mu_0 i }{2 \times 20 cm }\right)$
$\frac{ B _{ x }}{ B _{ y }}=\frac{1}{2}$