TS EAMCET 04 May 2019 Shift 1 Solved Paper

Consider the below diagram.
Let the radius of ring be r and thickness of the ring be dr The expression for the charge on the element is written as,
dq=σ(2πr)dr
The current associated with the rotatingcharge dq is calculated as

di‌‌=‌

dq

T

‌‌=‌

dqω

2π

This implies that,
di=σωrdr
The expression for the magnetic field at the centre is calculated as

dB‌‌=‌

µ0di

2r

‌‌=‌

µ0σωrdr

2r

‌‌=‌

µ0σωrd

2

Integratethe expression to calculate the net magnetic field as,
Bnet‌‌=‌

µ0σω

2

‌

R

∫

0

dr
‌‌=‌

µ0σω

2

dr