Answer:
1.389Ă—10^-5A
Explanation:
We can calculate the displacement current in the capacitor using the expresion below
J=Q/t---------------(*)
t= time elapsed
W= stored charge in capacitor
But Q= CV-----------(1)
C = capacitance across given capacitor
V =voltage across given capacitor.
But capacitance in parallel plate capacitor can be expressed vas
C= εA/d-----------(2)
A = area of plates
d= distance between the plates= 5.0 mm gap.= 5Ă—10^-3 m
ε= Vacuum permisivity= 8.85×10^-12F/m
If we input eqn (1) and (2) into eqn (*) we have the expression below
J= εAV/dt---------(4)
But ratio of V/t=500,000 V/s
But Area=Ď€d^2/2
Where d= diameter= (2Ă—radius)=(2Ă—5cm)=10cm=0.1m
Area=[ π × (0.1)^2]/2
=0.0157m^2
If we substitute all these value into eqn(4) we have
J=[( 8.85Ă—10^-12) Ă— (0.0157)Ă—(500,000)]/5Ă—10^-3
J=1.389Ă—10^-5A
Hence, the displacement current in the capacitor if the potential difference across the capacitor is increasing at 500,000 V/s is 1.389Ă—10^-5A
