# Post Problem Analysis - Rod in a cylindrical time varying magnetic field?

A metal rod of length $l$ is placed (as shown in figure) in a cylindrical time varying magnetic field. Find the potential difference across it.

As electric fields as forming circles around the centre with magnitude $$\frac12r\frac{dB}{dt}$$ whose magnitude is same along any chord at a fix distance from centre: $$\Delta V=E.l=\frac12r\frac32at^{\frac12}.l$$ $$\Delta V=\frac34arlt^{\frac12}$$

My question: Is $\Delta V =V_M-V_N$ or $\Delta V=V_N-V_M$ $\bf OR$ equivalently which side is at high potential?

Possible

• $(i)$ As Field lines are circular from $M$ to $N$, $M$ must be high potential.

• $(ii)$ As this field line apply a force on electrons- in the rod- towards left, then $M$ must have excess $e^-$ and $N$ must have deficiency; so $N$ would be high potential as $M$ is $(+)$ and $N$ is $(-)$.

• Did you check this one? – user22180 Aug 3 '14 at 14:51
• @user22180 yes it only tells to calculate field(that too not completely, which I know) but doesn't tell about higher potential... – RE60K Aug 5 '14 at 8:50
• That one tells you can't determine electric fields uniquely. Maybe you are taking some particular choice. If you tell on which choice your results are based, then it may be easy to tell about the higher potential. – user22180 Aug 5 '14 at 11:07
• I think it was not the magnitude but the component of Electric field along the chord that remains constant though. Not remember surely. – Mann May 7 '15 at 16:16