Introduction:
When a ring of radius r with linear charge density on its surface performs rotational motion about an axis perpendicular to its plane, it constitutes a current. In this explanation, we will determine the amount of current created by the ring.

Key Points:
To calculate the current, we need to consider the following key points:
1. Linear charge density on the surface of the ring.
2. Radius of the ring.
3. Rotational motion of the ring.
4. Angular velocity of the ring.

Calculating Current:
To calculate the current, we can use the formula for current (I = Q/t), where Q is the charge passing through a point in time t. In this case, we will consider the charge passing through the ring in a small time interval dt.

Differential Charge:
The differential charge dq on a small element of the ring is given by the product of the linear charge density and the length of the element. Since the ring is rotating, the length of the element can be considered as the circumference of the ring (2πr).

Differential Current:
The differential current di is given by the differential charge dq divided by the time interval dt. Therefore, di = dq/dt.

Calculating dq:
The differential charge dq is equal to the linear charge density multiplied by the length of the element. Since the element is a circular arc, the length of the element can be considered as the circumference of the ring (2πr). Therefore, dq = λ(2πr).

Calculating di:
The differential current di is equal to the differential charge dq divided by the time interval dt. Therefore, di = dq/dt = λ(2πr)/dt.

Calculating Total Current:
To calculate the total current, we need to integrate the differential current over the entire ring. The integration can be done from 0 to 2π, which represents a complete rotation of the ring.

Final Result:
The total current I is obtained by integrating the differential current over the entire ring. Therefore, I = ∫(λ(2πr)/dt) dθ, where θ represents the angle of rotation.

Conclusion:
In conclusion, the amount of current constituted by the ring of radius r with linear charge density on its surface performing rotational motion about an axis perpendicular to its plane can be calculated by integrating the differential current over the entire ring. By considering the differential charge and the time interval, we can determine the total current.

I = ∆q/∆t = 2πr (lemda)/(2π/Omega) = Omega*r*lemda