Q47 / 54 · JEE Advanced 2020 (Paper 1) · Physics

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)

Figure

  • Correct answer
    A
    I=V0tπρlnR2R1
  • B
    the outer surface is at a higher voltage than the inner surface
  • Correct answer
    C
    the outer surface is at a lower voltage than the inner surface
  • Correct answer
    D
    ΔV∝I2

Solution

Figure

Resistance of the strip =ρπrtdr

R=net resistance

1R=∫tdrρπrtπρ∫R1R2drr

R=πρtlnR2R1

Hence, current i =V0R=V0tπρlnR2R1

for elementary dr,

di=V0ρπrtdr=V0tdrρπr

i=nAev

V0tdrρπr=ntdrev

eE=mv2r=mV02n2ℓ2ρ2π2r2×1r

mv2r=mV02n2ℓ2ρ2π2r2×1r

E∝1r3

E=k1r3

ΔV=∫Edr=k∫R1R2drr2∝V02

∴  ∝  i2

Hence, the correct answer is options: 'A', 'C', 'D'.

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