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Question
Show that the magnetic field B at a point in between the plates of a parallel-plate capacitor during charging is `(ε_0mu_r)/2 (dE)/(dt)` (symbols having usual meaning).
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Solution
Let us assume Id be the displacement current in the region between two plates of parallel plate capacitor, in the figure.
The magnetic field at a point between two plates of capacitor at a perpendicular distance r from the axis of plates is given by
B = `(mu_0 2I_d)/(4pir) = mu_0/(2pir) I_d = mu_0/(2pir) xx ε_r (dphi_E)/(dt)` ......`[because I_d = (E_0dphi_E)/(dt)]`
⇒ B = `(mu_0ε_r)/(2pir) d/(dt) (Epir^2) = (mu_0ε_r)/(2pir) pir^2 (dF)/(dt)`
⇒ B = `(mu_0ε_r)/2 (dE)/(dt)` .....`[because phi_E = Epir^2]`
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