Q: In the e-book display described, each sphere has a dipole moment modeled as two opposite charges of $$3.5 \times 10$$^{-15}$$\ \text{C}$$ separated by $$100\ \mu\text{m}. If $$the electric field between the plates is $$4.0 \times 10^5$\ \text{N/C}$$, what is the maximum possible torque on a sphere?

$$1.4 \times 10$$^{-13}$$\ \text{N}\cdot\text{m}$$

Q: Electrons in a scanning electron microscope are accelerated through a $$30\ \text{kV}$$ potential difference. What is the speed of the electrons after acceleration?

$$1.0 \times 10^7$\ \text{m/s}$$

Question 1

Consider two point charges, $$q_1 = 10$$\ 	ext{nC}$$ and q_2$ = 20\ 	ext{nC}$$, placed a certain distance apart. Is there a point between them where the electric field is zero? If so, which charge is this point closer to?

Accepted Answer

Yes, and it is closer to the 10 nC charge.

Question 2

A parallel-plate capacitor is constructed of two square plates, size $$L 	imes L$$, separated by distance $$d. $$The plates are given charge $$\pm Q. $$What is the ratio $$E_f/E_i of $$the final electric field strength $$E_f to $$the initial electric field strength $$E_i if $$the length $$L of $$the plates is doubled, while $$Q$$ and $$d$$ remain constant?

Accepted Answer

$$E_f/E_i = 1/4$$

Question 3

A 0.50 g plastic bead with charge $$-6.0\ 	ext{nC} is $$suspended between two horizontal 12.0-cm-diameter circular plates. Which plate is positively charged?

Accepted Answer

The upper plate

Question 4

A positive charge is brought near a dipole as shown in the second image. If the dipole is free to rotate, what happens?

Accepted Answer

It begins to rotate in a clockwise direction.

Question 5

In the e-book display described, each sphere has a dipole moment modeled as two opposite charges of $$3.5 	imes 10$$^{-15}$$\ 	ext{C}$$ separated by $$100\ \mu	ext{m}. If $$the electric field between the plates is $$4.0 	imes 10^5$\ 	ext{N/C}$$, what is the maximum possible torque on a sphere?

Accepted Answer

$$1.4 	imes 10$$^{-13}$$\ 	ext{N}\cdot	ext{m}$$

Question 6

A 5.0 nC charge sits at $$x=0 in a $$uniform $$4500\ 	ext{N/C}$$ electric field directed to the right (see third image). At what point along the $$x-$$axis would a proton experience no net force?

Accepted Answer

$$x = -0.10\ 	ext{m}$$

Question 7

An electron $$q = -e$$ completes half of a circular orbit of radius $$r$$ around a nucleus with $$Q = +3e. By $$how much does the electric potential energy change as the electron moves from $$i to$$ $$f$$?

Accepted Answer

It does not change

Question 8

At one point in space, the electric potential energy of a $$15\ 	ext{nC}$$ charge is $$45\ \mu	ext{J}. $$What is the electric potential at this point?

Accepted Answer

$$3000\ 	ext{V}$$

Question 9

If a $$25\ 	ext{nC}$$ charge were placed at the same point as the previous question, what would its electric potential energy be?

Accepted Answer

$$75\ \mu	ext{J}$$

Question 10

Electrons in a scanning electron microscope are accelerated through a $$30\ 	ext{kV}$$ potential difference. What is the speed of the electrons after acceleration?

Accepted Answer

$$1.0 	imes 10^7$\ 	ext{m/s}$$

Question 11

An electron with an initial speed of $$500,000\ 	ext{m/s} is $$brought to rest by an electric field (see fourth image). Did the electron move into a region of higher potential or lower potential?

Accepted Answer

Lower potential

Question 12

What was the potential difference that stopped the electron with initial speed $$500,000\ 	ext{m/s}$$?

Accepted Answer

$$-0.71\ 	ext{V}$$

Question 13

What was the initial kinetic energy of the electron in electron volts (eV) if its speed was $$500,000\ 	ext{m/s}$$?

Accepted Answer

$$0.71\ 	ext{eV}$$

Question 14

A parallel-plate capacitor is constructed of two square plates, size $$L 	imes L$$, separated by distance $$d. $$The plates are given charge $$\pm Q. $$What is the ratio $$E_f/E_i of $$the final electric field strength $$E_f to $$the initial electric field strength $$E_i if $$the separation $$d is $$doubled, while $$Q$$ and $$L$$ remain constant?

Accepted Answer

$$E_f/E_i = 1$$

Question 15

A parallel-plate capacitor is constructed of two square plates, size $$L 	imes L$$, separated by distance $$d. $$The plates are given charge $$\pm Q. $$What is the ratio $$E_f/E_i of $$the final electric field strength $$E_f to $$the initial electric field strength $$E_i if $$the charge $$Q is $$doubled, while $$L$$ and $$d$$ remain constant?

Accepted Answer

$$E_f/E_i = 2$$

Question 16

A negatively charged bead is suspended between two parallel plates. If the bead is at rest, what must be true about the direction of the electric force relative to gravity?

Accepted Answer

The electric force must be upward, balancing gravity.

Question 17

A proton and an electron are placed at the same point along the x-axis in the presence of a uniform electric field and a stationary point charge. Where will both experience no net force?

Accepted Answer

At the same point where the electric field from the charge cancels the uniform field.

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