question_answer

A conducting disc of radius R rotating about its axis with an angular velocity \[\omega \]. Then the potential difference between the center of the disk and its edge is (no magnetic field is present)

A) zero                  

B)        \[\frac{{{m}_{e}}{{\omega }^{2}}{{R}^{2}}}{2e}\]

C) \[\frac{{{m}_{e}}{{\omega }^{2}}{{R}^{3}}}{2e}\]  

D)        \[\frac{e{{m}_{e}}\omega {{R}^{2}}}{2}\]

Correct Answer: B

Solution :

[b] \[eE={{m}_{e}}{{\omega }^{2}}r\] \[\Rightarrow \,\,\int_{{}}^{{}}{Edr=\frac{{{m}_{e}}{{\omega }^{2}}r}{e}\int_{0}^{R}{rdr}}\] \[\Rightarrow V=\frac{{{m}_{e}}{{\omega }^{2}}{{R}^{2}}}{2e}\]