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A metal rod of radius a is concentric with a metal cylindrical shell of radius b and length l. The space between rod and cylinder is tightly packed with a high resistance material of resistively ρ. A battery having a terminal voltage V is connected across the shown. Neglect resistance of rod and cylinder. If I is the total current in the circuit then:
1043727_448a690ec7784f33ad9a554e8aff3581.png

A
I=lVρ
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B
I=2πlVρ(1nb1na)
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C
I=4πlVρ(1nb1na)
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D
I=lV4πρ(1nb1na)
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Solution

The correct option is B I=2πlVρ(1nb1na)
6 metal rod if radius a is concentric with a
metal cylindrical shall of radius =b
Length=l
The space between rod and cylinder is tightly packet with high resistance material
ρ= resistivity
a battery having a terminal voltage =V
I= total current in the circuit
Let, radial flowest charge between rod and cylinder we have at ρ
J=I2πrland
E=ρI=ρl2πrl
With both J and E in the direction of α. Then the definition of the potential.
dV=EdsEdr=ρl2πl×dsV
And so nothing the polarity of Vf
Vf=r2r1dV=ρV2πlbαdrV=ρI2πlln(bα)
Solving for I
I=2πlVρ(lnblnα)

1227685_1043727_ans_acd39c14ff3548998a5ccd319da72838.png

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