A parallel-plate capacitor, made of two circular plates of radius R = 10 cm, is connected in series with a resistor of resistance R = 100 Ω and a battery of emf E = 10 V. What is the maximum value of the magnetic field induced by the displacement current between the plates, at a distance r = 5 cm from the axis of the plates while the capacitor is being charged?

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Costa

Physics

7 August, 04:29

A parallel-plate capacitor, made of two circular plates of radius R = 10 cm, is connected in series with a resistor of resistance R = 100 Ω and a battery of emf E = 10 V. What is the maximum value of the magnetic field induced by the displacement current between the plates, at a distance r = 5 cm from the axis of the plates while the capacitor is being charged?

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Patricia Wade · Answer 1

At the time when the capacitor starts charging, current through will be maximum.

Current in the circuit = 10 / 100 =.1 A.

This is called displacement current Id =.1 A.

magnetic field between the plates will be due to this displacement current.

Magnetic field lines will be circular in shape.

If B be the magnetic field, we shall apply ampere's circuital law to find magnetic field due to displacement current at a distance of 5 cm from axis.

∫ B dl = μ₀ Id

B x 2π x. 05 = 8.85 x 10⁻¹² x. 1

B = 2.82 x 10⁻¹² T.