Example of electromagnetic waves
Example 1: A parallel plate capacitor with plate area A and separation between the plates d is charged by a constant current I. consider a plane surface of area A/3 parallel to the plates and drawn symmetrically between the plates. Find the displacement current through this area.
Solution: Let Q be the charge on the capacitor at time t. The electric field intensity at a point in between the plates of the capacitor is:
E = Q/ϵ0A
The electric flux through the area considered is ɸE =(Q/ϵ0A)A/3=Q/3 ϵ0
The displacement current is
ID= ϵ0 ( dɸE/dt) = ϵ0 d/dt(Q/3 ϵ0) = ϵ0 × i/3 ϵ0 ( dQ/dt)= i/3
Example 2: find the energy stored in a 120 cm length of a laser beam operating at 6m W.
Solution: time taken by laser beam to move through a distance 120 cm is
T= 120/c=120/(3 × 1010) = 4 × 10-9 s
The energy contained in the 60 cm length of laser beam is
U = P × t=6 m W × (4 × 10-9 s )
=( 6 × 10-3 j/s) × (4 × 10-9 s)= 24 × 10-12 J
Ans: 24 × 10-12 J