A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is :

Question

1. zero at all places 2. constant between the plates and zero outside the plates 3. non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates 4. zero between the plates and non-zero outside

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Answer: 3. non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates Key idea: a changing electric field between the plates gives a displacement current, which produces a magnetic field by the Ampere-Maxwell law. Since σ increases steadily, E=σ/ε₀ changes at a constant rate. Using a circle of radius r coaxial with the plates: Inside ( r Outside ( r>R ): the whole displacement current is enclosed, so B∝1/r , which decreases with r . So B is non-zero everywhere, with its maximum at r=R , the cylindrical surface through the plate edges. Options 1, 2 and 4 are false.

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is :

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