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 :

• A

  zero at all places
• B

  constant between the plates and zero outside the plates
• Correct answer
  C

  non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates
• D

  zero between the plates and non-zero outside

Solution

$\begin{aligned} & I_d=\epsilon_0 \frac{d \phi_e}{d t}=\epsilon_0 \frac{d}{d t}\left(E A \cos 0^{\circ}\right) \\ & I_d=\epsilon_0 A \frac{d E}{d t} \\ & \because E=\frac{\sigma}{\epsilon_0} ; I_d=\epsilon_0 A \frac{d}{d t}\left(\frac{\sigma}{\epsilon_0}\right) \\ & \Rightarrow I_d=A\left(\frac{d \sigma}{d t}\right)=\text { constant } \end{aligned}$ Also $B$ due to $I_d$ is max ${ }^m$ at surface of imaginary cylinder

Hence, the correct answer is option: 'C'.