Magnetic field inside capacitor - is this right?

[bcjochim07]

Homework Statement

A 10 cm diameter parallel plate capacitor has a 1 mm spacing. The electric field between the plates is increasing at the rate of 1.0 * 10 ^6 V/ms. What is the magnetic field strength (a) on the axis (b) 3.0 cm from the axis

Homework Equations

The Attempt at a Solution

dE/dt = 1.0 e6
displacement current = dFlux/dt * permittivity constant = dE/dt * A * 8.85e-12
displacement current = 1.0e6 * pi * .05^2 * 8.85e-12 = 6.95e-8

The first part of the Ampere Maxwell equation falls out, leaving
B*s = displacement current

For on axis s= 0 , so is the magnetic field infinite?

3cm:
B*2pi*.03 = 6.95e-8 B = 3.688 e-7 T

Is this correct?

 

[bcjochim07]

actually I messed the problem up here. I got it now.

 

[thomate1]

I would say that your calculations appear to be mostly correct. However, there are a few things that could be clarified or expanded upon.

Firstly, it would be helpful to specify the units for each variable and to use consistent units throughout the calculation. For example, the electric field should be given in units of volts per meter (V/m) and the displacement current should be given in units of amperes (A).

Additionally, it would be helpful to explain the equations used and how they relate to the problem at hand. For example, you could mention that the displacement current is related to the change in electric field over time and is a key component in the Ampere-Maxwell equation, which relates magnetic fields to electric currents.

As for your question about the magnetic field being infinite on the axis, it is important to note that the magnetic field is not truly infinite, but rather becomes very large as the distance from the axis approaches zero. This is because the displacement current, and therefore the magnetic field, is directly proportional to the electric field, which is increasing at a very high rate in this problem.

Overall, your approach and calculations seem to be on the right track, but it would be beneficial to provide more context and explanation for each step.