A disc of radius `R` rotates at an angular velocity `omega` about the axis perpendicular to its surface and passing through its centre. If the disc has a uniform surface charge density `sigma`, find the magnetic induction on the axis of rotation at a distance `x` from the centre. (Given `R=3m`, `x=4m` and `mu_(0)sigmaomega=20Tesla//m`.)

Explanation

To find the magnetic induction (magnetic field) on the axis of rotation at a distance \( x \) from the center of a rotating disc with a uniform surface charge density \( \sigma \), we can follow these steps:

### Step 1: Define the Problem
We have a disc of radius \( R \) rotating with an angular velocity \( \omega \) and a uniform surface charge density \( \sigma \). We want to find the magnetic induction at a distance \( x \) from the center along the axis of rotation.

### Step 2: Consider a Differential Ring Element
To simplify the calculation, we can consider the disc as composed of an infinite number of concentric ring elements. Each ring has a radius \( r \) and thickness \( dr \).

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