How Does Charging a Capacitor Affect the Induced Magnetic Field?

[Sportsman4920]

Homework Statement

A 1400 nF capacitor with circular parallel plates 1.0 cm in diameter is accumulating charge at the rate of 25.0 mC/s at some instant in time. What will be the magnitude of the induced magnetic field 9.0 cm radially outward from the center of the plates?
T
What will be the magnitude of the field after the capacitor is fully charged?
T

Homework Equations

Obviously I'm a little confused, but I believe the general equation is B=mevE where B is magnetic field, e is c^2/Nxm^2, m is Nxs^2/C^2...on second, thought, I'm very confused.
another possibility is B=(mu) initial x I/ 2 pi r

The Attempt at a Solution

1400x25=35000x(1/9)=3888.89T

 

[marcusl]

Well some of your comments are on the right track. First you need to calculate the current, given the charge per second. Then use that current in your secon equation (often called the law of Biot and Savart).

However, don't forget to look at the units! You can't just plug in 25 without making use of its units milli-Coulomb.

 

[m2003]

I would first clarify the question to ensure that the units and variables are correct. It seems that the equation being used here is B = μ0I/2πr, where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the center of the plates.

Using this equation and the given values, the magnitude of the induced magnetic field at 9.0 cm from the center of the plates is:

B = (4π x 10^-7 Tm/A) x (25 x 10^-3 A) / (2π x 0.09 m) = 0.0013889 T

As for the second part of the question, once the capacitor is fully charged, the current will be zero and therefore the magnetic field will also be zero. This is because the magnetic field is only induced when there is a changing electric field, which is created by the current flowing through the circuit. Once the capacitor is fully charged, there is no longer a changing electric field and therefore no induced magnetic field.

In summary, the magnitude of the induced magnetic field at 9.0 cm from the center of the plates is 0.0013889 T, and the magnetic field will be zero after the capacitor is fully charged.