Q.

An infinite line charge of uniform electric charge  density  λ lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity  ε and electrical conductivity σ . The electrical conduction in the material follows Ohm’s law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material ?

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a

b

c

d

answer is D.

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Detailed Solution

j=Eσ⇒−12πrldqdt=λ2πε0rσ put q=λ/⇒−1λdλdt=σε0⇒∫Λ0λ dλλ=−σε0∫0t dt⇒ln⁡λλ0=−σtε0⇒λ=λ0e−σt/ε0 Now, j=Eσ=λ2πε0rσ=σ2πε0rλ0e−σtε0 "j decreases exponentially with time and j→0 as t→∞
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