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Question

# A long straight cable of length l is placed symmetrically along z-axis and has radius a(<<l). the cable consists of a thin wire and co-axial conducting tube. An alternating current I(t) = I0 sin (2πνt)flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is E(s, t) = μ0I0cos(2πνt) ln(sa)^k. The displacement current density inside the cable is

A
2πλ2I0ln(as)sin(2πνt)^k
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B
1λ2I0ln(as)sin(2πνt)^k
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C
πλ2I0ln(as)sin(2πνt)^l
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D
Zero
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Solution

## The correct option is B 2πλ2I0ln(as)sin(2πνt)^kGiven : The induced electric field at a distance from wire is E(s,t)=μ0I0vcos(2πvt)ln(sa)^kDisplacement current density is given by :→Jd=ϵ0dEdt⇒ϵ0μ0I0v∂∂(t)(cos2πvt)(sa)^kSubstitute for 1√μ0ϵ0⇒1c2I02πv2(−sin(2πvt))ln(sa)^k⇒(vc)22πI0sin(2πvt))ln(as)^k⇒2πλ2I0ln(as)sin(2πvt)^kOption (A) is correct.

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