Q: Which equation correctly expresses the magnitude of the electric field $$\vec{E}$$ created by a point charge $$q_{\text{source}} at a $$distance $$r in $$vacuum?

$$\vec{E} = \dfrac{k q_{\text{source}}}{r^2$}$$

Q: A test charge $$q_{\text{test}} = +1\ \text{C} is $$placed in the electric field of a source charge $$q_{\text{source}} = +3\ \text{C} at a $$distance of $$2\ \text{cm}. $$What is the magnitude of the force experienced by the test charge?

$$F = 8.99 \times 10^9$ \times \dfrac{3 \times 1}{0.02^2$}$$

Q: Two point charges, $$+3\ \text{C}$$ and $$-2\ \text{C}$$, are placed $$2\ \text{cm}$$ apart. What is the net electric field at a point $$1\ \text{cm} to $$the right of the $$+3\ \text{C}$$ charge?

$$E_{\text{net}} = k \left( \dfrac{3}{0.01^2$} + \dfrac{2}{0.01^2$} \right)$$

Q: A bead with charge $$+10 \times 10$$^{-9}$$\ \text{C} is at $$the origin. What is the magnitude of the electric field at the point $$(3.0\ \text{cm}, 4.0\ \text{cm})$$?

$$E = \dfrac{8.99 \times 10^9$ \times 10 \times 10$$^{-9}$$}{0.05^2$}$$

Q: Which formula gives the force on a test charge $$q$$ placed in an external electric field $$\vec{E}_{\text{external}}$$?

$$\vec{F} = q \vec{E}_{\text{external}}$$

Question 1

Which equation correctly expresses the magnitude of the electric field $$\vec{E}$$ created by a point charge $$q_{	ext{source}} at a $$distance $$r in $$vacuum?

Accepted Answer

$$\vec{E} = \dfrac{k q_{	ext{source}}}{r^2$}$$

Question 2

A test charge $$q_{	ext{test}} = +1\ 	ext{C} is $$placed in the electric field of a source charge $$q_{	ext{source}} = +3\ 	ext{C} at a $$distance of $$2\ 	ext{cm}. $$What is the magnitude of the force experienced by the test charge?

Accepted Answer

$$F = 8.99 	imes 10^9$ 	imes \dfrac{3 	imes 1}{0.02^2$}$$

Question 3

If the electric field at point A is $$E_A$$ due to a point charge, and point B is twice as far from the charge as point A, what is the electric field at point B?

Accepted Answer

$$E_B = \dfrac{E_A}{4}$$

Question 4

Two point charges, $$+3\ 	ext{C}$$ and $$-2\ 	ext{C}$$, are placed $$2\ 	ext{cm}$$ apart. What is the net electric field at a point $$1\ 	ext{cm} to $$the right of the $$+3\ 	ext{C}$$ charge?

Accepted Answer

$$E_{	ext{net}} = k \left( \dfrac{3}{0.01^2$} + \dfrac{2}{0.01^2$} ight)$$

Question 5

Which of the following best describes the direction of the electric field lines around a positive point charge?

Accepted Answer

They point radially outward away from the charge.

Question 6

A bead with charge $$+10 	imes 10$$^{-9}$$\ 	ext{C} is at $$the origin. What is the magnitude of the electric field at the point $$(3.0\ 	ext{cm}, 4.0\ 	ext{cm})$$?

Accepted Answer

$$E = \dfrac{8.99 	imes 10^9$ 	imes 10 	imes 10$$^{-9}$$}{0.05^2$}$$

Question 7

Which of the following changes would increase the electric field strength between two parallel plates with equal and opposite charges?

Accepted Answer

Increase the magnitude of the charge on both plates.

Question 8

What is the direction of the electric field at a point midway between two equal positive charges?

Accepted Answer

Zero; the fields cancel each other.

Question 9

Which formula gives the force on a test charge $$q$$ placed in an external electric field $$\vec{E}_{	ext{external}}$$?

Accepted Answer

$$\vec{F} = q \vec{E}_{	ext{external}}$$

Question 10

If the electric field at a point is $$\vec{E}$$ and a charge $$q is $$placed at that point, what is the direction of the force on the charge?

Accepted Answer

In the direction of $$\vec{E} if$$ $$q is $$positive, and opposite if $$q is $$negative.

Question 11

Which of the following statements about equipotential lines is correct?

Accepted Answer

Equipotential lines are perpendicular to electric field lines.

Question 12

A dipole consists of charges $$+q$$ and $$-q$$ separated by distance $$d. $$What is the direction of the electric field along the line connecting the charges, at a point closer to the positive charge?

Accepted Answer

Toward the negative charge.

Question 13

The electric field due to a proton at the position of an electron in a hydrogen atom ($$r = 0.53\ 	ext{nm}) is $$given by which formula?

Accepted Answer

$$E = \dfrac{k e}{r^2$}$$

Question 14

Which of the following best represents the electric field created by two positive charges placed near each other?

Accepted Answer

Field lines start at each charge and curve outward, never crossing.

Question 15

A heart generates a dipole electric field in the body. What is the primary medical application of measuring this field?

Accepted Answer

Diagnosing the condition of the heart using an electrocardiogram (ECG).

Question 16

If the electric field at a point is $$E = 200,000\ 	ext{N/C}$$ and a $$2.0\ 	ext{g}$$ charged object hangs at rest, what is the magnitude of the charge required to balance the gravitational force?

Accepted Answer

$$q = \dfrac{mg}{E}$$

Question 17

Which of the following is true about the relationship between electric field strength and distance from a point charge?

Accepted Answer

Electric field strength decreases as the inverse square of the distance.

Question 18

A test charge is placed at the midpoint between two equal but opposite charges. What is the direction of the net electric field at that point?

Accepted Answer

Toward the positive charge.

Question 19

Which constant is used in Coulomb's law and what is its value in SI units?

Accepted Answer

$$k = 8.99 	imes 10^9$\ 	ext{N} \cdot 	ext{m}^2 / 	ext{C}^2$$

Electric Fields and Forces: Study Notes

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