Question

The electric current in a circular coil of 2 turns produces a magnetic induction $B _1$ at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction $B _2$ at its centre. The ratio of $\frac{ B _2}{ B _1}$ is :

• A. $\frac{5}{2}$
• B. $\frac{25}{4}$
• C. $\frac{5}{4}$
• D. $\frac{25}{2}$

Answer 1

Answer: (B)

$ B =\frac{ N \mu_0 i }{2 R }$
$ B _1=\frac{ N _1 \mu_0 i }{2 R _1}$
For $ N _2=5$
Radius of coil $= R _2=\frac{ N _1 \times R _1}{ N _2}$
$ B _2=\frac{ N _2 \mu_0 i }{ R _2} $
$ \frac{ B _2}{ B _1}=\frac{ N _2}{ N _1} \cdot \frac{ R _1}{ R _2}=\frac{ N _2}{ N _1} \times \frac{ N _2}{ N _1} ; \frac{ B _2}{ B _1}=\frac{25}{4}$