Question 1

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

Accepted Answer

The field vectors point radially outward from the charge.

Question 2

Given the formula for the electric field between parallel plates $$E(y) = \frac{\sigma}{\$$epsilon_0$$} \hat{e}$$, what are the units of the product $$\sigma / \$$epsilon_0$$?

Accepted Answer

N/C (newtons per coulomb)

Question 3

In the field diagram of a dipole, what is the qualitative direction of the electric field at a point on the vertical axis above the positive charge?

Accepted Answer

The field points downward, toward the dipole axis.

Question 4

A parallel plate capacitor has plates separated by distance $$d$$ and area $$A. If $$the charge on the plates is $$Q$$, what is the magnitude of the electric field between the plates?

Accepted Answer

$$E = \frac{Q}{\$$epsilon_0$$ A}$$

Question 5

Which statement about field lines is correct?

Accepted Answer

Field lines always start on positive charges and end on negative charges.

Question 6

If the electric field at a point is $$\vec{E}$$, and you want to draw a field line through that point, what is the direction of the tangent to the field line at that point?

Accepted Answer

The tangent is parallel to $$\vec{E} at $$that point.

Question 7

Consider a dipole consisting of charges $$+q$$ and $$-q$$ separated by distance $$d. At a $$point far from the dipole, how does the magnitude of the electric field $$E$$ depend on the distance $$r$$ from the center of the dipole?

Accepted Answer

$$E \propto \frac{1}{r^3$}$$

Question 8

In the context of visualizing vector fields, what does a longer arrow at a sample point represent?

Accepted Answer

A larger magnitude of the vector field at that point.

Question 9

Which of the following is true about the electric field inside an ideal parallel plate capacitor?

Accepted Answer

The field is perpendicular to the plates and has constant magnitude.

Question 10

A helical curve is used to visualize a vector field. If the curve is parameterized by $$\vec{r}(t)$$, what does $$\frac{d\vec{r}}{dt}$$ represent?

Accepted Answer

The tangent vector to the curve at time $$t.$$

Question 11

If you want to reconstruct a field line numerically, which iterative formula would you use to find the next point $$\vec{r}_{n+1}$$ given the current point $$\vec{r}_n$$ and the field $$\vec{E}(\vec{r}_n)$$?

Accepted Answer

$$\vec{r}_{n+1} = \vec{r}_n + h \vec{E}(\vec{r}_n)$$

Question 12

Which of the following statements about the electric field of a negative point charge is correct?

Accepted Answer

The field vectors point radially inward toward the charge.

Question 13

In a field line diagram, what does the density of field lines indicate?

Accepted Answer

The magnitude of the field.

Question 14

If the surface charge density on a capacitor plate is $$\sigma$$ and the permittivity of free space is $$\$$epsilon_0$$, what is the electric field just outside the plate?

Accepted Answer

$$E = \frac{\sigma}{\$$epsilon_0$$}$$

Question 15

Which of the following is NOT a correct property of electric field lines?

Accepted Answer

Field lines can form closed loops in the presence of static charges.

Question 16

A student draws the electric field vectors for a dipole at several sample points. Which of the following best describes the pattern of the field vectors?

Accepted Answer

The vectors form a symmetric pattern, curving from the positive to the negative charge.

Question 17

In the context of a parallel plate capacitor, what happens to the electric field as you move from one plate to the other inside the capacitor?

Accepted Answer

The field remains constant in magnitude and direction.

Question 18

If you are given a field line diagram, what can you infer about the relative strength of the field at different locations?

Accepted Answer

Where field lines are closer together, the field is stronger.

Question 19

Which equation describes the tangent vector to a curve parameterized by $$\vec{r}(t)$$?

Accepted Answer

$$\frac{d\vec{r}}{dt}$$

Question 20

Suppose you want to estimate the number of electrons on a capacitor plate with charge $$Q. $$Which formula would you use?

Accepted Answer

$$N = \frac{Q}{e}$$

Visualizing Vector Fields in Physics: Electric Fields and Field Lines

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