Q.

Shown in the figure is a semicircular metallic strip that has thickness t and resistivity ρ . Its inner radius is R1 and outer radius is R2. If a voltage V0 is applied between its two ends, a current I flows in it. In addition, it is observed that a transverse voltage ΔV develops between its inner and outer surfaces due to purely kinetic effects of moving electrons (ignore any role of the magnetic field due to the current). Then (figure is schematic and not drawn to scale)-

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a

the outer surface is at a lower voltage than the inner surface

b

the outer surface is at a higher voltage than the inner surface

c

I=V0tπρlnR2R1

d

ΔVI2

answer is A, C, D.

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Detailed Solution

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All the elements are in parallel

l=πx and A=tdx

dx=ρπxtdx

1dr=R1R2tdxρπx1r=tπρlnR2R1 Resistance =πρtnR2R1

i=V0tlnR2R1πρ      (A)

(eE) will be inward direction in order to provide centripetal acceleration. Therefore electric field will be radially outward

Vouter <Vinner                  (C)mVd2r=qEE=mVd2qr I=neAVdVdiΔV=EdrΔVVd2ΔVI2

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