A closely wound coil has a radius of 6.00 cm and carries a current of `2.50 A`. How many turns must it have if, at a point on the coil axis `6.00 cm` from the centre of the coil, the magnetic field is `6.39 xx 10^-4T` ?

Explanation

To solve the problem, we will use the formula for the magnetic field along the axis of a closely wound coil (solenoid). The magnetic field \( B \) at a distance \( x \) from the center of the coil is given by:

\[ B = \frac{N \mu_0 I R^2}{2(R^2 + x^2)^{3/2}} \]

Where:
- \( N \) = number of turns
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