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Chapter 17: Problem 27

The displacement current flows in the dielectric of a capacitor (A) becomes zero. (B) has assumed a constant value. (C) is increasing with time. (D) is decreasing with time.

Short Answer

Expert verified
In the dielectric of a capacitor, the displacement current can either increase with time (C) when the capacitor is being charged, or decrease with time (D) when the capacitor is being discharged. Both options (C) and (D) are correct, depending on the specific scenario.

Step by step solution

01

Recall the concept of displacement current

Displacement current refers to a current that appears as if it is flowing through the dielectric in a capacitor, even though it does not involve the physical movement of charges. It is a time-varying electric field due to the changing electric flux through a dielectric material. The idea of displacement current was introduced by James Clerk Maxwell and is an essential concept in electromagnetism and the study of capacitors.
02

Relation between displacement current and the electric field

The displacement current density (J_d) inside the dielectric is proportional to the rate of change of the electric field (E) inside the dielectric material. It can be expressed using the following equation: \[J_d = \epsilon_0 \frac{\partial E}{\partial t}\] where \(\epsilon_0\) is the vacuum permittivity and t is time.
03

Analyze the given options

Now, let's analyze each option: (A) The displacement current becomes zero: If the rate of change of the electric field inside the dielectric is constant, then the displacement current will be zero. However, this situation is unlikely to occur in a capacitor as the electric field will change with time when the capacitor is being charged or discharged. (B) The displacement current has assumed a constant value: If the electric field inside the dielectric remains constant, then the displacement current will also be constant. However, this can only happen if the capacitor is charged and there is no change in the voltage across it. (C) The displacement current is increasing with time: If the electric field inside the dielectric is increasing with time, then the displacement current will also increase with time. This situation can occur when the capacitor is being charged. (D) The displacement current is decreasing with time: If the electric field inside the dielectric is decreasing with time, then the displacement current will also decrease with time. This situation can occur when the capacitor is being discharged.
04

Identify the correct option

From our analysis in Step 3, we can see that the displacement current in the dielectric of a capacitor can increase with time when the capacitor is being charged, and it can decrease with time when the capacitor is being discharged. Since the exercise mentions the flow of displacement current and not a specific case of charging or discharging the capacitor, both options (C) and (D) can be considered as correct depending on the specific scenario.

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