NEET · Physics · STD 12 - 8. Electromagnetic waves
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
- 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
Answer & Solution
Correct Answer
(C) non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates
Step-by-step Solution
Detailed explanation
\(I_d=\epsilon_0 \frac{d \phi_e}{d t}=\epsilon_0 \frac{d}{d t}\left(E A \cos 0^{\circ}\right) \)
\( I_d=\epsilon_0 A \frac{d E}{d t} \)
\( \because E=\frac{\sigma}{\epsilon_0} ; I_d=\epsilon_0 A \frac{d}{d t}\left(\frac{\sigma}{\epsilon_0}\right) \)
\( \Rightarrow I_d=A\left(\frac{d \sigma}{d t}\right)= constant\)
Also \(B\) due to \(I_d\) is \(\max ^m\) at surface of imaginary cylinder
\( I_d=\epsilon_0 A \frac{d E}{d t} \)
\( \because E=\frac{\sigma}{\epsilon_0} ; I_d=\epsilon_0 A \frac{d}{d t}\left(\frac{\sigma}{\epsilon_0}\right) \)
\( \Rightarrow I_d=A\left(\frac{d \sigma}{d t}\right)= constant\)
Also \(B\) due to \(I_d\) is \(\max ^m\) at surface of imaginary cylinder
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