does a magnetic field change the number of electrons, stored on a capacitor. No, because ... The purpose of a capacitor is not to store electrons but to store energy. A "charged" capacitor contains the same number of electrons as an "uncharged" capacitor. Electrons don't easily disappear or appear, they have to be moved somewhere.
From that it follows that the steady-state capacitance should be identical to that of the same capacitor outside the field. Or at least it would follow for a capacitor with vacuum between the plates. If there is a dielectric involved it we could at ask if the presence of the magnetic field has any effect on the dielectric constant of that material.
Since the capacitor plates are charging, the electric field between the two plates will be increasing and thus create a curly magnetic field. We will think about two cases: one that looks at the magnetic field inside the capacitor and one that looks at the magnetic field outside the capacitor.
Because the current is increasing the charge on the capacitor's plates, the electric field between the plates is increasing, and the rate of change of electric field gives the correct value for the field B found above. d dt
If you move the electrons around, you change the amount of stored energy, you don't change the capacitance. The capacitance depends on factors like plate-area, separation-distance and permittivity of separator. These are not normally affected by a magnetic field. From Wikipedia: "Capacitance is the ability of a body to store an electrical charge.
There cannot be a magnetic field outside the capacitor and nothing inside. However, applying this law to surface S2, which is bounded by exactly the same curve ∂ S, but lies between the plates, provides: B = . Any surface that intersects the wire has current I passing through it so Ampère's law gives the correct magnetic field.