A flat dielectric disc of radius `R` carries an exces charge on its surface. The surface charge density `sigma`. The disc rotastes about an axis perpendicular to its lane passing thrugh the centre with angulasr velocity `omega`. Find the toruque on the disc if it is placed in a uniform magnetic field `B` directed perpendicular to the rotation axis.
Text Solution
AI Generated Solution
To solve the problem of finding the torque on a rotating dielectric disc with a surface charge density in a magnetic field, we can follow these steps:
### Step 1: Understanding the Setup
We have a flat dielectric disc of radius \( R \) with a surface charge density \( \sigma \). The disc rotates about an axis perpendicular to its plane with an angular velocity \( \omega \). A uniform magnetic field \( B \) is directed perpendicular to the rotation axis.
### Step 2: Consider a Differential Element
We consider a small circular ring of radius \( r \) and thickness \( dr \) on the disc. The area of this ring is given by:
\[
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