A solenoid has a core of a material with relative permeability 400. The windings of the solenoid are insulated from the core and carry a current of 1 A. If the number of turns is 800 per metre, the magnetic field inside solenoid will be

0.40 T

The correct answer is Option (1) → 0.40 T

Given:

Relative permeability, $\mu_r = 400$

Current, $I = 1 \ \text{A}$

Number of turns per metre, $n = 800 \ \text{turns/m}$

Magnetic field inside a solenoid: $B = \mu_0 \mu_r n I$

Where $\mu_0 = 4\pi \times 10^{-7} \ \text{H/m}$

Substitute values:

$B = (4 \pi \times 10^{-7}) \cdot 400 \cdot 800 \cdot 1$

$B = 4 \pi \times 10^{-7} \cdot 320,000 = 1.28 \pi \times 10^{-1} \ \text{T}$

$B \approx 0.402 \ \text{T}$

Magnetic field inside solenoid: $B \approx 0.402 \ \text{T}$