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)

$B=\frac{N{\mu }_{0}i}{2R}$
$B_1=\frac{N_1{\mu }_{0}i}{2R_1}$
For $N_2=5$
Radius of coil $=R_2=\frac{N_1\times R_1}{N_2}$
$B_2=\frac{N_2{\mu }_{0}i}{R_2}$
$\frac{B_2}{B_1}=\frac{N_2}{N_1}\cdot \frac{R_1}{R_2}=\frac{N_2}{N_1}\times \frac{N_2}{N_1};\frac{B_2}{B_1}=\frac{25}{4}$