Em Waves Question 68
Question: A parallel plate capacitor with plate area A and separation between the plates J, is charged by a constant current i. Consider a plane surface of area all parallel to the plates and drawn simultaneously between the plates. The displacement current through this area is
Options:
A) $ i $
B) $ i/2 $
C) $ i/4 $
D) $ i/8 $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Charge on Capacitor plates at time t is, q=it Electric field between the plates at this instant. $ E=\frac{q}{A{\varepsilon _{0}}}=\frac{it}{A{\varepsilon _{0}}} $ Electric flux through the given area $ {\phi _{E}}=( \frac{A}{2} )E=\frac{it}{2{\varepsilon _{0}}} $
Therefore, displacement current $ i _{d}={\varepsilon _{0}}\frac{d{\phi _{E}}}{dt}={\varepsilon _{0}}\frac{d}{dt}( \frac{it}{2{\varepsilon _{0}}} )=\frac{i}{2} $
BETA
