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A solenoid is a long coil containing large number of close turns of insulated metal wire.

The magnetic field at the center of the solenoid.

The magnetic field at the center of the solenoid is given by

$\begin{array}{r}B={渭}_{0}nl\\ B={渭}_0\frac{N}{L}l\end{array}$

Where, B is the magnetic field at the center of solenoid ,${渭}_0$ is the permeability of vaccum which is equal to$4\mathrm{蟺}脳{10}^{-7}\mathrm{T}.\mathrm{m}/\mathrm{A}$ , l is the current passing through the solenoid , n is the number of turns per unit length.

Given: The current passing through the coil is l = 2.00A .

The length of the solenoid is L = 500cm .

The total number of turns is N = 1000 .

Using

$\begin{array}{r}B={渭}_{0}nI\\ B={渭}_0\frac{N}{L}I\end{array}$

Now, putting the values of constants in above expression

$\begin{array}{r}B=\left(4蟺脳{10}^{鈭�7}\mathrm{T}.\mathrm{m}/\mathrm{A}\right)脳\frac{1000}{5\mathrm{m}}脳2.00\mathrm{A}\\ B=5.03脳{10}^{鈭�4}\mathrm{T}\end{array}$

Thus, the magnetic field at the center of the solenoid is$5.03脳{10}^{-4}T$