1. Magnetic field inside a solenoid

For a solenoid, the magnetizing field is $H = nI$ where

• $H$ = magnetic field intensity in $A/m$
• $n$ = number of turns per unit length
• $I$ = current

2. Given data

• Coercivity required for demagnetization: $H_c = 3 \times 10^3\, A/m$
• Length of solenoid: $L = 10\,cm = 0.1\,m$
• Number of turns: $N = 100$

So turns per unit length: $n = \frac{N}{L} = \frac{100}{0.1} = 1000\, m^{-1}$

3. Condition for demagnetization

To demagnetize the magnet, the solenoid must produce a magnetic field intensity equal to coercivity: $H = H_c$ So, $nI = 3 \times 10^3$ $1000 \cdot I = 3000$ $I = \frac{3000}{1000} = 3\,A$

4. Match with options

The required current is $\boxed{3\,A}$ So the correct option is C.