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Show that the magnetic field B at a poin...

Show that the magnetic field B at a point in between the plates of a parallel plate capacitor during charging is `B=(mu_(0)in_(0)r)/(2).(dE)/(dt)` (symbols having usual meaning).

Text Solution

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Consider current `I_(d)` between plates of parallel plate capacitor.

Magnetic field at perpendicular distance r from one plate of capacitor,
`B=(mu_(0)I)/(2pi r)=(mu_(0))/(2pi r)I_(d)=(mu_(0))/(2pi r)xx(in_(0)(d phi_(E ))/(dt)) " " [because I_(d)=in_(0)(d phi_(E ))/(dt)]`
`=(mu_(0)in_(0))/(2pi r)[(d)/(dt)(E pi r^(2))]`
`=(mu_(0)in_(0))/(2pi r).pi r^(2)(dE)/(dt)`
`B=(mu_(0)in_(0)r)/(2).(dE)/(dt)[because phi_(E )=EA=E xx pi r^(2)]`
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