A permanent magnet has a coercive force of 4.0 × 10^4 A m^ -1 . It...

The coercive force $H_c$ is the magnetic field intensity required to completely demagnetize the magnet.

For a long solenoid, the magnetic field intensity $H$ is given by $H = nI$, where $n$ is the number of turns per unit length and $I$ is the current.

Given:
$H_c = 4.0 \times 10^4 \text{ A m}^{-1}$
$n = 40 \text{ turns/cm} = 4000 \text{ turns/m}$

Equating $H$ to $H_c$ to find the required current:
$nI = H_c$

$4000 \times I = 4.0 \times 10^4$

$I = \dfrac{40000}{4000} = 10 \text{ A}$