Question

A circular coil has one turn and carries a current $i$. The same wire is wound into a smaller coil of $4$ turns and the same current is passed through it. Field at the center

• A. decreases to $1/4$ of the value
• B. is the same
• C. increases to $14$ times the values
• D. increases to $16$ times the values

Answer 1

Answer: (D)

increases to $16$ times the values

$B=\frac{{\mu }_{0}Ni}{2r}$
So, length of the wire is same. So, $r$ will be decreased by $4$ times since $N$ is increased by $4$ times.
So, $B_1=\frac{{\mu }_{0}4Ni}{2r/4}$
$=\frac{{\mu }_{0}Ni}{2r}16$
$=16B$
So, field increases by $16$ times.