To analyze which statement is true about Ampere's law as it applies to a parallel plate capacitor, let’s first break down the relevant concepts:

Ampere's Law and the Parallel Plate Capacitor

Ampere’s law, in its modified form due to Maxwell’s correction, can be written as:

$\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 ( I + \epsilon_0 \frac{d\Phi_E}{dt} )$

This equation includes the displacement current term ($\epsilon_0 \frac{d\Phi_E}{dt}$), which accounts for the changing electric field between the plates of a capacitor when it is charging or discharging.

Breakdown of the Statements:

1. When the capacitor is fully charged there will be a magnetic field that has a larger magnitude at the edge of the plate compared to the center.

   • This statement is false. When a capacitor is fully charged, there is no current flowing, hence no changing electric field between the plates. Therefore, there would be no magnetic field in the space surrounding the plates.

2. When the capacitor is charging or discharging there will be a magnetic field that has a larger magnitude at the center compared to the edge of the plate.

   • This statement is false. The magnetic field around the plates of a charging or discharging capacitor is determined by the displacement current, which is symmetric. The field is generally stronger near the edges of the plates due to the fringing effects of the electric field, not the center.

3. When the capacitor is fully charged there will be a magnetic field that has a larger magnitude at the center compared to the edge of the plate.

   • This statement is false. When the capacitor is fully charged, there is no changing electric field or real current, so there is no magnetic field.

4. The displacement current referenced in Ampere's law is only a way for us to be consistent with Kirchhoff's rules, there is nothing measurable in the space between the capacitor plates.

   • This statement is false. The displacement current is a real concept introduced to make Maxwell's equations consistent. While it is not a "current" in the traditional sense (involving moving charges), it represents the changing electric field between the plates, which can give rise to a measurable magnetic field.

5. When the capacitor is charging or discharging there will be a magnetic field that has a larger magnitude at the edge of the plate compared to the center.

   • This statement is true. When the capacitor is charging or discharging, the magnetic field is produced due to the changing electric field (displacement current) between the plates. The magnetic field tends to be stronger near the edges of the plates due to the non-uniform fringing fields at the edges.

Correct Answer:

The correct statement is: When the capacitor is charging or discharging there will be a magnetic field that has a larger magnitude at the edge of the plate compared to the center.

Would you like a more detailed explanation, or do you have any further questions?

5 Related Questions:

1. How does the displacement current contribute to Ampere’s law?
2. What is the physical interpretation of the displacement current in a parallel plate capacitor?
3. How do fringing effects influence the magnetic field near the edges of a capacitor?
4. How is Ampere’s law modified by Maxwell’s correction for time-varying electric fields?
5. What role does symmetry play in the magnetic field distribution in a charging capacitor?

Tip:

Remember that displacement current is essential for making Maxwell’s equations consistent with the conservation of charge, especially in regions where no actual charge is moving, such as between the plates of a charging capacitor.