Understanding capacitors

Two plates of equal and opposite charge are set into the configurations above. Choose the configuration of the plates that will produce the maximum capacity with the greatest capacity to store energy. The vertical separation between plates is same in all cases .

D B A C

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3 solutions

Josh Silverman Staff
Aug 12, 2015

First, recall that capacitance is simply the charge imbalance one must produce between two conductors to achieve a potential difference of one Volt between them. Because excess charge must be spread evenly across surface of a conductor, the capacitance C C a pure function of the geometry of the two conductors.

Consider the case when we have one of the plates in isolation, and give it some charge Q Q . The charge distributes itself around the surface so that the net force on each particle is zero. If any given charge were to deviate a small distance from its position in this arrangement, other charges would quickly start to flow until the net force on each particle went back to zero. Thus, charges on the conductor's surface feel a strong pressure not to get closer to one another.

Now, consider the case where we bring two plates next to each other such that they form a cross as in C. In this arrangement, the charges in the region of overlap interact and generate a field of strength roughly equal to E 1 4 π ε 0 2 σ Δ A d 2 E\approx\displaystyle \frac{1}{4\pi\varepsilon_0}\frac{2\sigma \Delta A}{d^2} where d d is the distance of separation, σ \sigma is the local charge density on the surface in the region of overlap, and Δ A \Delta A is the area of the surface patch.

If it were possible to bring all the charge in each plates into the region of overlap, we could generate a large voltage between the two plates locally, but this is not possible since the local repulsion between the positive and negative charges within each place tends to spread charge all along the plates. Thus, the charge in the region of overlap has a small separation, generates a large field, thus a large voltage. However, the charge elsewhere in the plates is separated from charges in the other plate by a large distance, thus, outside the region of the interaction, the field and voltage is much smaller.

Andriane Casuga
Aug 10, 2015

B.....because energy stored in capacitor is given by the relation E=1/2 cv^2 that means capacitance is directly proportional to energy stored .and also C= ( permitivity*area)/d , here area means overlapping area between two plates which is directly proportional to capacitance C, here fig B have more overlapping area hence stores more energy.

Mudit Singh
Aug 14, 2015

i think the answer is changed ... can anyone guide me ?

I think it is too. Which means those who correctly answered it earlier get no credit.

Ian Turnbull - 5 years, 10 months ago

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