CHAPTER 1 - Fundamentals of Electrical Circuits
8
The magnetic field at a distance from the central axis of the capacitor may therefore be expressed
by equation (1.4-8)
The capacitance is defined as
Where is the voltage across the capacitor. Such a voltage may be easily calculated by means of
equation (1.2-1), since the Electric field inside the capacitor is uniform
∫ ∫
hence from (1.4-9) and (1.4-10)
( )
( )
Where is the distance between the capacitor plates. By substituting (1.3-2) and (1.4-11)(b) into
(1.4-8) we obtain
( )
( )
( )
Equation (1.4-12) shows that the capacitance relates the magnitude of the magnetic field and
the rate of change of the magnitude of the electric field inside a capacitor (
⁄
), at a specific
point in space defined by the radial distance from its axis, in a linear fashion. It also shows how the
magnetic field is related to the first derivative of the electric field, just like the current though a
capacitor is related to the first derivative of the voltage across it (equation (1.4-1)(b)).
1.4-2 Electric and Magnetic Fields for a parallel plate capacitor
(1.4-8)
(1.4-9)
(1.4-11)
(1.4-12)
(1.4-10)
+
-
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