Question

32.3 displacement current
the displacement current at a point in space depends upon
the difference in the number of protons vs electrons at that point.
the number of electrons passing that point per unit time.
the number of electrons at that point.
the rate at which the electric field at that point changes with time.

Explanation:

The displacement current \(I_d\) is given by the formula \(I_d=\epsilon_0\frac{d\Phi_E}{dt}\), where \(\Phi_E\) is the electric flux (\(\Phi_E = E\cdot A\), \(E\) is the electric field and \(A\) is the area). If the area \(A\) is constant (in a simple case), \(I_d=\epsilon_0 A\frac{dE}{dt}\). So, the displacement current depends on the rate of change of the electric field with time.

• The difference in the number of protons and electrons relates to charge density, not displacement current.
• The number of electrons passing per unit time is conduction current (\(I = \frac{dq}{dt}\), where \(q = ne\), \(n\) is the number of electrons and \(e\) is the elementary charge).
• The number of electrons at a point is just a charge quantity, not related to displacement current.

Answer:

the rate at which the electric field at that point changes with time.