# Magnetic Field in parallel plate capacitor

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1. Mar 17, 2016

### LoveBoy

1. The problem statement, all variables and given/known data
A parallel plate capacitor of area 60cm^2 and separation 3mm is charged initially at 90 micro coulomb. If the medium between the plates get slightly conducting and the plate loses charge initially at the rate of 2.5 *10^-8 C per sec then what is the magnetic field between the plates?

2. Relevant equations

3. The attempt at a solution
My Attempt :-
I don't if i am correct or wrong.
I think Magnetic field would be zero at initial condition and final condition . But i don't know how do i calculate magnetic field at any instant ?

2. Mar 17, 2016

### Staff: Mentor

Welcome to the PF.

Is there a figure that goes along with this problem? There will be a circulating magnetic field around the leakage current lines, but that's parallel to the plates, not "between" the plates (subject to interpretation -- hence my question about the figure)...

3. Mar 17, 2016

### LoveBoy

Well there is no figure.Simply a detailed question.Options are not there too.

4. Mar 18, 2016

### Staff: Mentor

Well, then I guess we need to assume that "between" means with any orientation, not necessarily pointing between the plates (which the B-field does not do here).

Are you familiar with the calculation of the magnetic fiend using Ampere's Law for the B-field inside and outside a current-carrying wire (assuming a constant current distribution within the wire, which is similar to your problem here)?

5. Mar 18, 2016

### LoveBoy

Well, i know the formula.But didn't apply at all cuz i'm in grade 12.

6. Mar 19, 2016

### Staff: Mentor

Do they say why? It's not zero in the direction that is parallel to the plates. They must be asking about in the direction of the current, perpendicular to the plates..?

7. Mar 20, 2016

### LoveBoy

Well this is what i know. Answer is zero and no additional information is given in question.

8. Mar 20, 2016

### Staff: Mentor

If we picture the space between the plates as being filled with dozens of conducting (albeit resistive) wires 'shorting' the plates, won't their magnetic fields cancel, except around the fringes of the medium?

9. Mar 20, 2016

### LoveBoy

10. Mar 20, 2016

### Staff: Mentor

I believe this situation is the same as the one I mentioned earlier -- it's like when you calculate the B-field strength both inside and outside of a uniform current-carrying wire. It increases with radius until you reach the boundary of the wire, and decreases with r after that. It's calculated via Ampere's Law.

EDIT -- So I believe the full answer is that there is a B-field parallel to the plates, there is none perpendicular to the plates, "between" them...

11. Mar 22, 2016

### Staff: Mentor

On reviewing this, I'd say it's likely that the question was set by someone who didn't fully understand what is involved in answering it.

As berkeman says, it involves the application of Amperes Law. The maths is beyond HS level, but there's a graph midway through this article: http://dev.physicslab.org/document.aspx?doctype=3&filename=magnetism_ampereslaw.xml

In summary, the magnetic field is not zero except along the centreline in the gap.

12. Mar 22, 2016

### LoveBoy

13. Mar 22, 2016

### rude man

The magnetic field lines are circles about the center of the plates, and the field strength is proportional to the radial distance away from the center.

This is an approximate statement since the plates' sides are not infinitely large It also assumes that the leakage current is uniform across the area of the plates.
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