1.

A time varying magnetic field is present in a cylindrical region of radius R as shown in figure ( cross - sectionalview ). B is increasing with time, mark out the correct statement (s) for the given situation, r being the distance from centre of cylindrical region.

Answer»

For `rltR`, the INDUCED electric field is proportional to `r`
For `rgtR`, the induced electric field is proprotional to `(1)/(R )`
For `r=R`, the induced electric field is maximum
If a coaxial "non- conducting"RING of radius `(R )/(2)` is placed in the magnetic field region, then emf induced in the ring is `(PI alpha R^(2))/(4)`

Solution :For `rleR,2pir=(dB)/(dt)xxpir^(2)`
`impliesE=(alphar)/(2)` For `rgtR,Exx2pir=(dB)/(dt)xxpiR^(2)`
`impliesE=(alphaR^(2))/(2R)` For `r=(R)/(2),` the emf induced,
`e=(dB)/(dt)xxpi((R)/2)^(2)=(pi alphaR^(2))/(4)`


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