Question

Curves in the graph shown give, as functions of radial distance r, the magnitude B of the magnetic field inside and outside four long wires a, b, c and d, carrying currents that are uniformly distributed across the cross-sections of the wires. Overlapping portions of the plots are indicated by double labels. Which wire has the greatest radius?

• A. a
• B. b
• C. c
• D. d

Answer 1

The correct option is C c

Inside the cylinder: $B.2\pi =\mu \frac{I}{\pi R^2}\pi r^2$

$\Rightarrow B=\frac{{\mu }_{0}I}{2\pi R^2}.r$ ........ (1)

Outside the cylinder: $B.2\pi r={\mu }_{0}I$

$\Rightarrow B=\frac{{\mu }_{0}I}{2\pi r}$ .......... (2)

Inside the cylinder $B\propto r$ and outside $B\propto \frac{1}{r}$
So, from surface nature of magnetic field changes.
Hence, it is clear from the graph that wire 'c' has greatest radius.