A thin wire is wound very tightly in one layer on the surface of a sphere of paramagnetic material `(mu_(r)~~1)`. The planes of all the turns can be assumed to be perpendicular to the same diameter of the sphere. The turns over the entire surface of the sphere. The radius of the sphere is `R`, the total number of turns is `N`, and the current in the winding is `I`. Find the magnetic induction at the centre of the sphere. (Given `mu_(0)NI=20R`)

Explanation

To solve the problem of finding the magnetic induction at the center of a sphere wound with a thin wire, we can follow these steps:

### Step 1: Understand the Geometry
We have a sphere of radius \( R \) with a thin wire wound tightly around it in one layer. The wire creates \( N \) turns, and the current flowing through the wire is \( I \). The planes of the wire turns are perpendicular to a diameter of the sphere.

**Hint:** Visualize the sphere and the wire wrapped around it. Recognize that the wire creates a magnetic field due to the current flowing through it.

### Step 2: Determine the Magnetic Field Contribution from a Ring
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