How Do You Solve This Capacitor Problem with Aluminum Electrodes?

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The problem involves calculating the capacitance of two aluminum electrodes with a diameter of 5.0 cm and a separation of 0.50 mm, connected to a 200 V battery. The capacitance formula C = εA/d was applied, with the area calculated as π * (d^2/4). The user obtained a capacitance of 139 pF, but the online homework platform indicated this result was incorrect. The discussion highlights a potential error in the area calculation, suggesting a review of the formula used for the area of the electrodes. Accurate calculations are crucial for determining the correct capacitance value.
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Homework Statement


Two 5.0-cm-diameter aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 200 V battery.

Homework Equations


C = εA/d

The Attempt at a Solution


So for my solution I took the area of the plate, ((.052π) * 8.85*10-12) / .5*10-3 and I got an answer of 1.39 * 10-10 F or 139 pF. The website the homework is done through is saying this is wrong. not too sure where the mistake is...
 
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Area of electrode = pi * d^2 /4

Looks like you used pi * d^2
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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