A parallel plate capacitor with circular plates of radius 10 cm has a capacitance of 50 F . It is being charged by a source such that the potential difference across its plates is changing at a rate of 20 V s ⁻¹ . The magnitude of the induced magnetic field exactly at the outer edge of the capacitor plates is: (Given ₀ = 4 10⁻⁷ T m A ⁻¹ )

Step-by-step solution

The displacement current between the capacitor plates is given by: I_d = C dV dt I_d = 50 10⁻⁶ 20 = 10⁻³ A According to the Ampere-Maxwell law, the line integral of the magnetic field around the edge of the plates is equal to ₀ times the total displacement current enclosed: B d l = ₀ I_d B(2 R) = ₀ I_d Substituting the given values ( R = 10 cm = 0.1 m ): B = ₀ I_d 2 R B = 4 10⁻⁷ 10⁻³ 2 0.1 B = 2 10⁻¹⁰ 0.1 = 2 10⁻⁹ T Option 1 is incorrect as a changing electric field induces a magnetic field even in the absence of c