NEETPhysicsElectromagnetic Waves
A circular parallel plate capacitor of radius R is being charged such that the electric field between the plates changes at a uniform rate. Which of the following correctly describes the variation of the induced magnetic field B with the radial distance r from the central axis of the plates?
Options
- AB increases linearly with r for r R .
- BB is constant for r R .
- CB is zero for r R .
- DB increases as r^2 for r R .
Correct answer
A. B increases linearly with r for r R .
Step-by-step solution
According to the Ampere-Maxwell law, the line integral of the magnetic field along a circular Amperian loop of radius r is B d l = ₀ I_ d, enclosed . For a point inside the capacitor ( r Therefore, B(2 r) = ₀ I_d r^2 R^2 B = ( ₀ I_d 2 R^2 ) r . This shows that B increases linearly with r for r For a point outside the capacitor ( r > R ), the enclosed displacement current is the total displacement current I_d . Therefore, B(2 r) = ₀ I_d B = ₀ I_d 2 r . This shows that B decreases as 1/r for r > R . Hence, the magnet