Question

Curve in the graph shown give, as functions of radius 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 pots 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

Let the radius of the wire be $R$.

Magnetic field inside wire at a distance $r$ is given by

${\mu }_0{I}_{enc}=B\left(2\pi r\right)$

$⟹B_{in}=\frac{{\mu }_0(j\times \pi r^2)}{2\pi r}$

$={\mu }_{0}jr/2$

Magnetic field outside the wire=$B_{out}=\frac{{\mu }_0\left(j\pi R^2\right)}{2\pi r}$

$={\mu }_{0}j{R}^2/\left(2r\right)$

Therefore magnetic field at the surface of wire=${\mu }_{0}jR/2$
Clearly the point of non-differentiation of curve is at the radius of the wire.