Exam 17: Electric Potential

$\mathrm { A } + 7.5 - \mathrm { nC }$ point charge is $5.0 \mathrm {~cm}$ from a $- 9.4 - \mu \mathrm { C }$ point charge in your laboratory in California. How much work would you have to do if you left the $+ 7.5 - \mathrm { nC }$ charge in the lab but took the $- 9.4 - \mu \mathrm { C }$ charge to New York City? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

If the result of your calculations for a quantity has $\mathrm { SI }$ units of $\mathrm { C } ^ { 2 } \cdot \mathrm { s } ^ { 2 } / \left( \mathrm { kg } \cdot \mathrm { m } ^ { 2 } \right)$ , that quantity could be

When a 12.0-V battery causes $2.00 \mu \mathrm { C }$ of charge to flow onto the plates of an air-filled capacitor, how much work did the battery do?

Point charges $+ 4.00 \mu \mathrm { C }$ and $+ 2.00 \mu \mathrm { C }$ are placed at the opposite corners of a rectangle as shown in the figure. What is the potential at point B due to these charges? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \right.$ . $\mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

The potential difference between two square parallel plates is $4.00 \mathrm {~V}$ . If the plate separation is $6.00 \mathrm {~cm}$ and they each measure $1.5 \mathrm {~m}$ by $1.5 \mathrm {~m}$ , what is the magnitude of the electric field between the plates?

When a 4- $\mu \mathrm { F }$ capacitor has a potential drop of $20 \mathrm {~V}$ across its plates, how much electric potential energy is stored in this capacitor?

A $5.0 \mu \mathrm { F }$ capacitor has a potential difference of $5.0 \mathrm {~V}$ applied across its plates. If the potential difference across its plates is increased to $8.0 \mathrm {~V}$ , how much additional energy does the capacitor store?

The square plates of a $3000 - \mathrm { pF }$ parallel-plate capacitor measure $40 \mathrm {~mm}$ by $40 \mathrm {~mm}$ and are separated by a dielectric that is $0.29 \mathrm {~mm}$ thick and completely fills the region between the plates. What is the dielectric constant of the dielectric? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

A uniform electric field, with a magnitude of $500 \mathrm {~V} / \mathrm { m }$ , is points in the $+ x$ direction. If the potential at $x = 5.0 \mathrm {~m}$ is $2500 \mathrm {~V}$ , what is the potential at $x = 2.0 \mathrm {~m}$ ?

An alpha particle (a helium nucleus, having charge $+ 2 e$ and mass $6.64 \times 10 ^ { - 27 } \mathrm {~kg}$ ) moves head-on at a fixed gold nucleus (having charge $+ 79 e$ ). If the distance of closest approach is $2.0 \times 10 ^ { - 10 } \mathrm {~m}$ , what was the speed of the alpha particle when it was very far away from the gold? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = \right.$ $\left. 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

$\mathrm { A } + 4.0 - \mu \mathrm { C }$ and a $- 4.0 - \mu \mathrm { C }$ point charge are placed as shown in the figure. What is the potential difference between points $A$ and $B$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$

A region of space contains a uniform electric field, directed toward the right, as shown in the figure. Which statement about this situation is correct?

In a region where the electric field is uniform and points in the $+ x$ direction, the electric potential is $- 2000 \mathrm {~V}$ at $x = 8 \mathrm {~m}$ and is $+ 400 \mathrm {~V}$ at $x = 2 \mathrm {~m}$ . What is the magnitude of the electric field?

A tiny particle with charge $+ 5.0 \mu \mathrm { C }$ is initially moving at $55 \mathrm {~m} / \mathrm { s }$ . It is then accelerated through a potential difference of $500 \mathrm {~V}$ . How much kinetic energy does this particle gain during the period of acceleration?

Two tiny grains of sand having charges of $4.0 \mu \mathrm { C }$ and $- 4.0 \mu \mathrm { C }$ are situated along the $x$ -axis at $x _ { 1 } =$ $2.0 \mathrm {~m}$ and $x _ { 2 } = - 2.0 \mathrm {~m}$ . What is electric potential energy of these grains relative to infinity? $( k = 1 / 4$ $\pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

A small $4.0 - \mu C$ charge and a small $1.5 - \mu C$ charge are initially very far apart. How much work does it take to bring them to a final configuration in which the $4.0 - \mu \mathrm { C }$ charge is at the point $x = 1.0$ $\mathrm { mm } , y = 1.0 \mathrm {~mm}$ , and the $1.5 - \mu \mathrm { C }$ charge is at the point $x = 1.0 \mathrm {~mm} , y = 3.0 \mathrm {~mm}$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \right.$ $\times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 }$ )

An air-filled parallel-plate capacitor is constructed with a plate area of $0.40 \mathrm {~m} ^ { 2 }$ and a plate separation of $0.10 \mathrm {~mm}$ . It is then charged to a potential difference of $12 \mathrm {~V}$ ? $\left( \varepsilon _ { 0 } = 8.85 \times \right.$ $10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 }$ ) (a) How much charge is stored on each of its plates? (b) How much energy is stored in it?

A $12.6 - \mu \mathrm { F }$ isolated capacitor is constructed with Teflon, having a dielectric constant of $2.1$ , between the plates. The capacitor is initially charged to $1.5$ volts, and then the Teflon is removed. (a) How much excess charge was originally stored on the plates of the capacitor? (b) After removing the Teflon, what is the potential difference across the capacitor plates?

Each plate of an ideal air-filled parallel-plate capacitor has an area of $0.0010 \mathrm {~m} ^ { 2 }$ , and the separation of the plates is $0.050 \mathrm {~mm}$ . An electric field of $7.4 \times 10 ^ { 6 } \mathrm {~V} / \mathrm { m }$ is present between the plates. What is the capacitance of this capacitor? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

Point charges $+ 4.00 \mu \mathrm { C }$ and $+ 2.00 \mu \mathrm { C }$ are placed at the opposite corners of a rectangle as shown in the figure. What is the potential difference $V _ { \mathrm { A } } - V _ { \mathrm { B } }$ ? $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 8.99 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$