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A conductor is made of an isotropic mate...

A conductor is made of an isotropic material and has shape of a truncated cone. A battery of constant emf is connected across it and its left end is earthed as shown. If at a certain section at a distance x form left end, electric field intensity and the rate of generation of heat per unit length are E and H respectively, which of the following graphs is (are) correct?

A

B

C

D

Text Solution

Verified by Experts


`r=a+((b-a)/l)x`
Let p resistivity of the material
`implies` Resistance of the cone =`int_0^l (p dx)/([a+(b-a)/l)x]^2)=(pl)/(pi ab)`
`implies `i= current flowing in the wire =`(pi abV)/(pl)`
Rotating charge is equivalent to current `dx implies dR=(pdx)/(pi[a+(b-c)/l) x]^2)`
`implies dv=idR implies dV=i (pdx)/A` where `A=pi[a+(b-a)/l)x]^2`
`implies E=(dV)/(dx)=(p i)/A implies` B is correct and `H=i^2dR implies (dQ)/(dx)=i^2 p/A implies` (D) is correct
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