|Class 12 Physics Electromagnetic Waves||Displacement Current|
It arises due to the fixed charges.
It arises due to the change in electric field.
Ampere – Maxwell law: Consequences
Case 1 : Magnetic field is given as
Case 2 : Magnetic field is given as
Problem:- Figure shows a capacitor made of two circular plates each ofradius 12 cm, and separated by 5.0 cm. The capacitor is beingcharged by an external source (not shown in the figure). Thecharging current is constant and equal to 0.15A.(a) Calculate the capacitance and the rate of charge of potentialdifference between the plates.
(b) Obtain the displacement current across the plates.
(c) Is Kirchhoff’s first rule (junction rule) valid at each plate of thecapacitor? Explain
Radius of each circular plate, r = 12 cm = 0.12 m
Distance between the plates, d = 5 cm = 0.05 m
Charging current, I = 0.15 A
Permittivity of free spaceε0, = 8.85 × 10−12 C2 N−1 m−2
(a) Capacitance between the two plates is given by the relation,
C = (ε0A)/ (d)
A = Area of each plate=πr2
C= (ε0πr2)/ (d)
= (8.85x10-12πx0.12x0.12)/ (0.05)
Charge on each plate, q = CV
V = Potential difference across the plates
Differentiation on both sides with respect to time (t) gives:
Bur (dq/dt) =current (I)
Therefore (dV/dt) = (I/C)
=> (0.15)/ (80.032x10-12) =1.87 ×109 V/s
Therefore, the change in potential difference between the plates is 1.87 ×109 V/s.
(b) The displacement current across the plates is the same as the conduction current. Hence, the displacement current, id is 0.15 A.
Kirchhoff’s first rule is valid at each plate of the capacitor provided that we take the sum of conduction and displacement for current.