First find ∮RB⃗ ⋅dl⃗ , the line integral of B⃗ around a loop of radius R located just outside the left capacitor plate. This can be found from the usual current due to moving charge in Ampère's law, that is, without the displacement current. Find an expression for this integral involving the current I(t) and any needed constants given in the introduction.

the expression of current in the loop enclosed to the left of the capacitor plate is

Explanation:

As we know by Ampere's law that line integral of magnetic field around a closed loop is proportional to the current enclosed in the path

So we will have

so we have

so above is the expression of current in the loop enclosed to the left of the capacitor plate

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