Q: What is the minimum magnitude of an electric field that balances the weight of a plastic sphere of mass $$2.4\ \mathrm{g}$$ that has been charged to $$4.5\ \mu\mathrm{C}$$?

$$6.4 \times 10^6$\ \mathrm{N/C}$$

Q: Two point charges of $$+20.0\ \mu\mathrm{C}$$ and $$-8.00\ \mu\mathrm{C}$$ are separated by a distance of $$20.0\ \mathrm{cm}. $$What is the magnitude of the electric field due to these charges at a point midway between them?

$$25.2 \times 10^6$\ \mathrm{N/C}$$ directed toward the negative charge

Question 1

Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude $$F$$ due to the other. With time, charge gradually leaks off of both spheres. When each of the spheres has lost half its initial charge, what is the new magnitude of the electrostatic force between them?

Accepted Answer

$$\frac{1}{4}F$$

Question 2

Refer to the first image (two spheres in a test tube, distance $$d$$ apart). If the charge on each ball is doubled, what happens to the equilibrium distance between the balls?

Accepted Answer

$$2d$$

Question 3

Three equal negative point charges are placed at three corners of a square of side $$d as $$shown in the second image. Which arrow represents the direction of the net electric field at the center of the square?

Accepted Answer

A

Question 4

A small sphere with a mass of $$441\ \mathrm{g} is $$moving upward along the vertical $$+y-$$axis when it encounters an electric field of $$5.00\ \mathrm{N/C}. If$$, due to this field, the sphere suddenly acquires a horizontal acceleration of $$13.0\ \mathrm{m/s^2$}$$, what is the charge that it carries?

Accepted Answer

$$-1.15\ \mathrm{C}$$

Question 5

What is the minimum magnitude of an electric field that balances the weight of a plastic sphere of mass $$2.4\ \mathrm{g}$$ that has been charged to $$4.5\ \mu\mathrm{C}$$?

Accepted Answer

$$6.4 	imes 10^6$\ \mathrm{N/C}$$

Question 6

Two point charges of $$+20.0\ \mu\mathrm{C}$$ and $$-8.00\ \mu\mathrm{C}$$ are separated by a distance of $$20.0\ \mathrm{cm}. $$What is the magnitude of the electric field due to these charges at a point midway between them?

Accepted Answer

$$25.2 	imes 10^6$\ \mathrm{N/C}$$ directed toward the negative charge

Question 7

Two flat $$4.0\ \mathrm{cm} 	imes 4.0\ \mathrm{cm}$$ electrodes carrying equal but opposite charges are spaced $$2.0\ \mathrm{mm}$$ apart with their midpoints opposite each other. Between the electrodes but not near their edges, the electric field strength is $$2.5 	imes 10^6$\ \mathrm{N/C}. $$What is the magnitude of the charge on each electrode?

Accepted Answer

$$16\ \mathrm{nC}$$

Question 8

If a rectangular area is rotated in a uniform electric field from the position where the maximum electric flux goes through it to an orientation where only half the flux goes through it, what has been the angle of rotation?

Accepted Answer

$$45^\circ$$

Question 9

Refer to the third image (uniform electric field directed to the right). Which statement about the electric potential is true?

Accepted Answer

The potential at point A is the highest, the potential at point B is the second highest, and the potential at point C is the lowest.

Question 10

Suppose you have two point charges of opposite sign. As you move them farther and farther apart, the potential energy of this system relative to infinity:

Accepted Answer

decreases.

Question 11

A very small object carrying $$-6.0\ \mu\mathrm{C} of $$charge is attracted to a large, well-anchored, positively charged object. How much kinetic energy does the negatively charged object gain if the potential difference through which it moves is $$3.0\ \mathrm{mV}$$?

Accepted Answer

$$18\ \mathrm{nJ}$$

Question 12

The electric field between the plates of a parallel-plate capacitor has magnitude $$E. $$The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation. What is the new magnitude of the electric field between the plates?

Accepted Answer

$$E/2$$

Question 13

A vertical wire carries a current straight down. To the east of this wire, the magnetic field points:

Accepted Answer

toward the north.

Question 14

A horizontal wire carries a current straight toward you. From your point of view, the magnetic field at a point directly below the wire points:

Accepted Answer

directly toward you.

Question 15

Two very long parallel wires are a distance $$d$$ apart and carry equal currents in opposite directions. The locations where the net magnetic field due to these currents is equal to zero are:

Accepted Answer

a distance $$d to $$the left of the left wire and also a distance $$d to $$the right of the right wire.

Question 16

Refer to the fourth image (two charged spheres suspended by threads). If the angle $$	heta$$ increases, what does this indicate about the magnitude of the charge on the spheres?

Accepted Answer

The charge has increased.

Question 17

Refer to the fifth image (electron projected between parallel plates). If the electron is projected from plate A toward plate B with an initial velocity $$v_0$$, what is the final velocity of the electron as it strikes plate B? (Neglect relativistic effects.)

Accepted Answer

$$v = \sqrt{v_0$^2 + 2eEd/m}$$

Question 18

Refer to the sixth image (cone in a uniform electric field). If the electric field is $$E$$ and the sloping side surface area is $$A$$, what is the electric flux through the sloping side surface?

Accepted Answer

$$\Phi = EA\cos	heta$$

Question 19

Refer to the seventh image (graph of $$V vs$$ $$r). $$What is the electric field $$E as a $$function of $$r$$ between $$r=1 m $$and $$r=3 m$$?

Accepted Answer

$$E = -\frac{dV}{dr} = -2\ \mathrm{V/m}$$

Question 20

Refer to the eighth image (three point charges on the x-axis, point P above the center). What is the electric potential at point P due to these charges?

Accepted Answer

$$V = \frac{1}{4\pi\$$epsilon_0$$} \left( \frac{-2.00\ \mu\mathrm{C}}{\sqrt{(0.2)^2$ + (0.2)^2$}} + \frac{4.00\ \mu\mathrm{C}}{0.2} + \frac{6.00\ \mu\mathrm{C}}{\sqrt{(0.2)^2$ + (0.2)^2$}} \right)$$

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