Chapter 17: Electric Potential

Four identical point charges are arranged at the corners of a square [Hint: Draw a figure]. The electric field E and potential V at the centre of the square are

(a) $E=0$, $V=0$.

(b) $E=0$, $V\ne 0$.

(c) $E\ne 0$, $V\ne 0$.

(d) $E\ne 0$, $V=0$.

(e) $E=V$ regardless of the value.

State clearly the difference (a) between electric potential and electric field, (b) between electric potential and electric potential energy.

(II) An electric field of $\mathbf{8}\mathbf{.50}\times \mathbf{1}{\mathbf{0}}^{\mathbf{5}}\mathbf{V}\mathbf{/}\mathbf{m}$ is desired between two parallel plates, each of area $\mathbf{45}\mathbf{.0}\mathbf{c}{\mathbf{m}}^{\mathbf{2}}$ and separated by 2.45 mm of air. What charge must be on each plate?

(II) If a capacitor has opposite $\mathbf{4}\mathbf{.2}\mu \mathbf{C}$ charges on the plates, and an electric field of $\mathbf{2}\mathbf{.0}\mathbf{k}\mathbf{V}\mathbf{/}\mathbf{m}\mathbf{m}$ is desired between the plates, what must each plate’s area be?

(II) It takes 18 J of energy to move a 0.30-mC charge from one plate of a $\mathbf{15}\mu \mathbf{F}$ capacitor to the other. How much charge is on each plate?

(II) To get an idea how big a farad is, suppose you want to make a 1-F air-filled parallel-plate capacitor for a circuit you are building. To make it a reasonable size, suppose you limit the plate area to . What would the gap have to be between the plates? Is this practically achievable?

(II) How strong is the electric field between the plates of a $\mathbf{0}\mathbf{.80}\mu \mathbf{F}$ air-gap capacitor if they are 2.0 mm apart and each has a charge of $\mathbf{62}\mu \mathbf{C}$?

(III) A $\mathbf{2}\mathbf{.50}\mu \mathbf{F}$ capacitor is charged to 746 V and a $\mathbf{6}\mathbf{.80}\mu \mathbf{F}$ capacitor is charged to 562 V. These capacitors are then disconnected from their batteries. Next the positive plates are connected to each other and the negative plates are connected to each other. What will be the potential difference across each and the charge on each? [Hint: Charge is conserved.]

Question: (I) What is the capacitance of two square parallel plates 6.6 cm on a side that are separated by 1.8 mm of paraffin?

Question: (I) What is the capacitance of a pair of circular plates with a radius of 5.0 cm separated by 2.8 mm of mica?