A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5 A. The magnetic flux density produced by the solenoid is: (Permeability of free space = $$4\pi \times 10^{-7}$$ H m$$^{-1}$$)

The magnetic flux density inside a solenoid with a core of relative permeability $$\mu_r$$ is given by $$B = \mu_r \mu_0 n I$$, where $$n$$ is the number of turns per metre and $$I$$ is the current.

Substituting the given values: $$B = 500 \times 4\pi \times 10^{-7} \times 1000 \times 5$$. Computing step by step: $$4\pi \times 10^{-7} \times 1000 = 4\pi \times 10^{-4}$$, then $$500 \times 4\pi \times 10^{-4} = 2000\pi \times 10^{-4} = 0.2\pi$$, and finally $$0.2\pi \times 5 = \pi$$ T.

The correct answer is option 1: $$\pi$$ T.