Question

A solid cylindrical wire of radius $R$ carries a current $I$. The ratio of magnetic fields at points which are located at $R/2$ and $2R$ distance away from the axis of the wire:

• A. 1:1
• B. 1:2
• C. 2:1
• D. 1:4

Answer 1

The correct option is A 1:1

Given: Radius=r, Current=I

Solution: The formula used for solid cylindrical wire :

Outside the cylinder:

$B_{out}=\frac{{\mu }_{0}I}{2\pi r}(r>R)$

Here r=2R

$B_{out}=\frac{{\mu }_{0}I}{2\pi \times 2R}(r=2R)$ ......(1)

Inside the cylinder:

$B_{in}=\frac{{\mu }_{0}I\times r}{2\pi \times R^2}(r<R)$

$B_{in}=\frac{{\mu }_{0}I}{2\pi \times 2\times R}(r=\frac{R}{2})$......(2)

$\frac{B_{in}}{B_{out}}=1:1$

Hence the correct option is A