Exam 17: Electric Potential

A battery maintains the electrical potential difference of $6.0 - \mathrm { V }$ between two large parallel metal plates separated by $1.0 \mathrm {~mm}$ . What is the strength of the electric field between the plates?

A proton with a speed of $2.0 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$ accelerates through a potential difference and thereby increases its speed to $4.0 \times 10 ^ { 5 } \mathrm {~m} / \mathrm { s }$ . Through what magnitude potential difference did the proton accelerate? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {proton } } = 1.67 \times 10 ^ { - 27 } \mathrm {~kg} \right)$

A sphere with radius $2.0 \mathrm {~mm}$ carries a $+ 2.0 \mu \mathrm { C }$ charge. What is the potential difference, $V _ { B } - V _ { A }$ , between point $\mathrm { B }$ , which is $4.0 \mathrm {~m}$ from the center of the sphere, and point $\mathrm { A }$ , which is $6.0 \mathrm {~m}$ from the center of the sphere? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

An ideal air-filled parallel-plate capacitor consists of two circular plates, each of radius $0.30 \mathrm {~mm}$ . How far apart should the plates be for the capacitance to be $300.0 - \mathrm { pF } ? \left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \right.$ $\mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 }$ )

When a certain capacitor carries charges of $\pm 10 \mu \mathrm { C }$ on its plates, the potential difference cross the plates is $25 \mathrm {~V}$ . Which of the following statements about this capacitor are true? (There could be more than one correct choice.)

At a distance $d$ from a point charge $Q$ , the energy density in its electric field is $u$ . If we double the charge, what is the energy density at the same point?

Four charged particles (two having a charge $+ Q$ and two having a charge $- Q$ ) are arranged in the $x y$ -plane as shown in the figure. The charges are all equidistant from the origin. The amount of work required to move a positively charged particle from point $P$ to point $O$ (both of which are on the $z$ -axis) is

The equipotential surfaces for two point charges are shown in the figure, with the value of potential marked on the line for each surface. (a) What is the potential difference, $V _ { G } - V _ { D }$ , between points $G$ and D? (b) What is the potential difference, $V$ A - $V _ { \mathrm { G } }$ , between points $\mathrm { A }$ and $\mathrm { G }$ ?

If you want to store $2.0 \mathrm {~mJ}$ of energy in a $10 - \mu \mathrm { F }$ capacitor, how much potential do you need to put across it?

A $7.0 - \mu \mathrm { C }$ point charge and a $9.0 - \mu \mathrm { C }$ point charge are initially extremely far apart. How much work does it take to bring the $7.0 - \mu C$ point charge to the point $x = 3.0 \mathrm {~mm} , y = 0.0 \mathrm {~mm}$ , and the $9.0 - \mu \mathrm { C }$ point charge to the point $x = - 3.0 \mathrm {~mm} , y = 0.0 \mathrm {~mm} ? \left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

Two parallel plates that are initially uncharged are separated by $1.7 \mathrm {~mm}$ , have only air between them, and each have surface areas of $16 \mathrm {~cm} ^ { 2 }$ . How much charge must be transferred from one plate to the other if $1.9 \mathrm {~J}$ of energy are to be stored in the plates? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } 2 / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

How much work is needed to carry an electron from the positive terminal to the negative terminal of a $9.0 - \mathrm { V }$ battery. $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

Two large parallel plates are separated by $1.0 \mathrm {~mm}$ of air. If the potential difference between them is $3.0 \mathrm {~V}$ , what is the magnitude of their surface charge densities? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

Two point charges of $+ 2.00 \mu \mathrm { C }$ and $+ 4.00 \mu \mathrm { C }$ are at the origin and at the point $x = 0.000 \mathrm {~m} , y =$ $- 0.300 \mathrm {~m}$ , as shown in the figure. What is the electric potential due to these charges, relative to infinity, at the point $\mathrm { P }$ at $x = 0.400 \mathrm {~m}$ on the $x$ -axis? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

When the potential difference between the plates of an ideal air-filled parallel plate capacitor is 35 $\mathrm { V }$ , the electric field between the plates has a strength of $750 \mathrm {~V} / \mathrm { m }$ . If the plate area is $4.0 \times 10 ^ { - 2 } \mathrm {~m} ^ { 2 }$ , what is the capacitance of this capacitor? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } 2 / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

A spherical oil droplet with nine excess electrons is held stationary in an electric field between two large horizontal plates that are $2.25 \mathrm {~cm}$ apart. The field is produced by maintaining a potential difference of $0.3375 \mathrm { kV }$ across the plates, and the density of the oil is $824 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ . What is the radius of the oil drop? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

How much kinetic energy does a proton gain if it is accelerated, with no friction, through a potential difference of $1.00 \mathrm {~V}$ ? The proton is 1836 times heavier than an electron, and $e = 1.60 \times10^{-19}$ C.

An ideal parallel-plate capacitor has a capacitance of $C$ . If the area of the plates is doubled and the distance between the plates is halved, what is the new capacitance?

A tiny particle carries a charge of $6.0 \mu \mathrm { C }$ . What is the energy density in the electric field at a distance of $4.0 \mathrm {~m}$ from this charge? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } , k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

When a $6.00 - \mu \mathrm { F }$ air-filled capacitor has a charge of $\pm 40.0 \mu \mathrm { C }$ on its plates, how much potential energy is stored in this capacitor?