Question

A length $L$ of wire carries steady current $I$. It is bent first to form a cylinder plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the center caused by the same current is

• A. A quarter of its first value
• B. Unaltered
• C. Four times of its first value
• D. A half of its first value

Answer 1

The correct option is C Four times of its first value

$2\pi R=L$

And, $2\left(2\pi r\right)=L$

$B_1=\frac{{\mu }_{0}I}{2R}=\frac{{\mu }_{0}I\times \pi }{L}$

$B_2=\left(\frac{{\mu }_{0}I}{2r}\right)\times 2=\frac{{\mu }_{0}I\times 4\pi }{L}$

$\therefore B_2=4B_1$