## Related questions with answers

A 0.200-A current is charging a capacitor that has circular plates 10.0 cm in radius. If the plate separation is 4.00 mm (a) what is the time rate of increase of electric field between the plates? (b) What is the magnetic field between the plates 5.00 cm from the center?

Solution

Verified(a) $\textbf{Calculation: }$

Solve for the capacitor:

Solve for the time rate of increase of electric field between the plates:

According to Gauss law of electric flux:

$\begin{align*} \Phi_{E} &= \dfrac{ q}{ \varepsilon_{0} } \\ \end{align*}$

Differentiate both sides with respect to the time $t$:

$\begin{align*} \dfrac{ d\Phi_{E}}{ dt} &= \dfrac{ dq}{ dt} \dfrac{ 1}{ \varepsilon_{0} } \\ \end{align*}$

In order to evaluate the electric current, we use the following relation:

$\begin{align*} I &= \dfrac{ dq}{ dt} \end{align*}$

Substituting from the previous calculation, then we get

$\begin{align*} \dfrac{ d\Phi_{E}}{ dt} &= \dfrac{ dq}{ dt} \dfrac{ 1}{ \varepsilon_{0} } \\ &= \dfrac{ I}{ \varepsilon_{0} } \\ \end{align*}$

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