A 0.5 m long solenoid has 500 turns and has a flux density of $2.52 × 10^{-3} T$ at its centre. The current flowing in the solenoid would be

(given, $μ_0 = 4 π × 10^{-7} Hm^{-1}$)

2.0 A

The correct answer is Option (1) → 2.0 A

Given:

Length of solenoid, $l = 0.5\,m$

Number of turns, $N = 500$

Magnetic flux density, $B = 2.52 \times 10^{-3}\,T$

Permeability of free space, $\mu_0 = 4\pi \times 10^{-7}\,H/m$

Magnetic field inside a solenoid:

$B = \mu_0 n I$, where $n = \frac{N}{l}$

Therefore,

$I = \frac{B}{\mu_0 n} = \frac{B \, l}{\mu_0 N}$

Substitute values:

$I = \frac{2.52 \times 10^{-3} \times 0.5}{4\pi \times 10^{-7} \times 500}$

$I = \frac{1.26 \times 10^{-3}}{2\pi \times 10^{-4}}$

$I = \frac{1.26 \times 10^{-3}}{6.283 \times 10^{-4}} = 2.0\,A$

Final Answer: $I = 2.0\,A$