Electrostatics 7 Question 5

5. 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? (a)

(c)

(b)

(d)

Show Answer

Solution:

Suppose charger per unit length at any instant is λ

Initial value of λ is suppose λ0.

Electric field at a distance r at any instant is

E=λ2πεrJ=σE=σλ2πεri=dqdt=J(A)=Jσ2πrldλldt=λ2πεr×σ2πrlλdλ=σεatdt

λ=λ0eαεtJ=σ2πεrλ=σλ02πεreσεt=J0eσεt Here, J0=σλ02πεr

J(t) decreases exponentially as shown in figure below.



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक